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Aşağıdaki liste integrallerini içermektedir integral fonksiyonlarının tüm bir listesi için lütfen integral tabl

Hiperbolik fonksiyonların integralleri

Hiperbolik fonksiyonların integralleri
www.wikipedia.tr-tr.nina.azhttps://www.wikipedia.tr-tr.nina.az

Aşağıdaki liste integrallerini içermektedir. İntegral fonksiyonlarının tüm bir listesi için lütfen İntegral tablosu sayfasına bakınız.

c sabiti sıfırdan farklı varsayılmıştır.

∫sinh⁡cxdx=1ccosh⁡cx{\displaystyle \int \sinh cx\,dx={\frac {1}{c}}\cosh cx}{\displaystyle \int \sinh cx\,dx={\frac {1}{c}}\cosh cx}
∫cosh⁡cxdx=1csinh⁡cx{\displaystyle \int \cosh cx\,dx={\frac {1}{c}}\sinh cx}{\displaystyle \int \cosh cx\,dx={\frac {1}{c}}\sinh cx}
∫sinh2⁡cxdx=14csinh⁡2cx−x2{\displaystyle \int \sinh ^{2}cx\,dx={\frac {1}{4c}}\sinh 2cx-{\frac {x}{2}}}{\displaystyle \int \sinh ^{2}cx\,dx={\frac {1}{4c}}\sinh 2cx-{\frac {x}{2}}}
∫cosh2⁡cxdx=14csinh⁡2cx+x2{\displaystyle \int \cosh ^{2}cx\,dx={\frac {1}{4c}}\sinh 2cx+{\frac {x}{2}}}{\displaystyle \int \cosh ^{2}cx\,dx={\frac {1}{4c}}\sinh 2cx+{\frac {x}{2}}}
∫tanh2⁡cxdx=x−tanh⁡cxc{\displaystyle \int \tanh ^{2}cx\,dx=x-{\frac {\tanh cx}{c}}}{\displaystyle \int \tanh ^{2}cx\,dx=x-{\frac {\tanh cx}{c}}}
∫sinhn⁡cxdx=1cnsinhn−1⁡cxcosh⁡cx−n−1n∫sinhn−2⁡cxdx(for n>0){\displaystyle \int \sinh ^{n}cx\,dx={\frac {1}{cn}}\sinh ^{n-1}cx\cosh cx-{\frac {n-1}{n}}\int \sinh ^{n-2}cx\,dx\qquad {\mbox{(for }}n>0{\mbox{)}}}{\displaystyle \int \sinh ^{n}cx\,dx={\frac {1}{cn}}\sinh ^{n-1}cx\cosh cx-{\frac {n-1}{n}}\int \sinh ^{n-2}cx\,dx\qquad {\mbox{(for }}n>0{\mbox{)}}}
Ayrıca: ∫sinhn⁡cxdx=1c(n+1)sinhn+1⁡cxcosh⁡cx−n+2n+1∫sinhn+2⁡cxdx(for n<0, n≠−1){\displaystyle \int \sinh ^{n}cx\,dx={\frac {1}{c(n+1)}}\sinh ^{n+1}cx\cosh cx-{\frac {n+2}{n+1}}\int \sinh ^{n+2}cx\,dx\qquad {\mbox{(for }}n<0{\mbox{, }}n\neq -1{\mbox{)}}}{\displaystyle \int \sinh ^{n}cx\,dx={\frac {1}{c(n+1)}}\sinh ^{n+1}cx\cosh cx-{\frac {n+2}{n+1}}\int \sinh ^{n+2}cx\,dx\qquad {\mbox{(for }}n<0{\mbox{, }}n\neq -1{\mbox{)}}}
∫coshn⁡cxdx=1cnsinh⁡cxcoshn−1⁡cx+n−1n∫coshn−2⁡cxdx(for n>0){\displaystyle \int \cosh ^{n}cx\,dx={\frac {1}{cn}}\sinh cx\cosh ^{n-1}cx+{\frac {n-1}{n}}\int \cosh ^{n-2}cx\,dx\qquad {\mbox{(for }}n>0{\mbox{)}}}{\displaystyle \int \cosh ^{n}cx\,dx={\frac {1}{cn}}\sinh cx\cosh ^{n-1}cx+{\frac {n-1}{n}}\int \cosh ^{n-2}cx\,dx\qquad {\mbox{(for }}n>0{\mbox{)}}}
Ayrıca: ∫coshn⁡cxdx=−1c(n+1)sinh⁡cxcoshn+1⁡cx−n+2n+1∫coshn+2⁡cxdx(for n<0, n≠−1){\displaystyle \int \cosh ^{n}cx\,dx=-{\frac {1}{c(n+1)}}\sinh cx\cosh ^{n+1}cx-{\frac {n+2}{n+1}}\int \cosh ^{n+2}cx\,dx\qquad {\mbox{(for }}n<0{\mbox{, }}n\neq -1{\mbox{)}}}{\displaystyle \int \cosh ^{n}cx\,dx=-{\frac {1}{c(n+1)}}\sinh cx\cosh ^{n+1}cx-{\frac {n+2}{n+1}}\int \cosh ^{n+2}cx\,dx\qquad {\mbox{(for }}n<0{\mbox{, }}n\neq -1{\mbox{)}}}
∫dxsinh⁡cx=1cln⁡|tanh⁡cx2|{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|\tanh {\frac {cx}{2}}\right|}{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|\tanh {\frac {cx}{2}}\right|}
Ayrıca: ∫dxsinh⁡cx=1cln⁡|cosh⁡cx−1sinh⁡cx|{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\cosh cx-1}{\sinh cx}}\right|}{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\cosh cx-1}{\sinh cx}}\right|}
Ayrıca: ∫dxsinh⁡cx=1cln⁡|sinh⁡cxcosh⁡cx+1|{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\sinh cx}{\cosh cx+1}}\right|}{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\sinh cx}{\cosh cx+1}}\right|}
Ayrıca: ∫dxsinh⁡cx=1cln⁡|cosh⁡cx−1cosh⁡cx+1|{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\cosh cx-1}{\cosh cx+1}}\right|}{\displaystyle \int {\frac {dx}{\sinh cx}}={\frac {1}{c}}\ln \left|{\frac {\cosh cx-1}{\cosh cx+1}}\right|}
∫dxcosh⁡cx=2carctan⁡ecx{\displaystyle \int {\frac {dx}{\cosh cx}}={\frac {2}{c}}\arctan e^{cx}}{\displaystyle \int {\frac {dx}{\cosh cx}}={\frac {2}{c}}\arctan e^{cx}}
∫dxsinhn⁡cx=cosh⁡cxc(n−1)sinhn−1⁡cx−n−2n−1∫dxsinhn−2⁡cx(for n≠1){\displaystyle \int {\frac {dx}{\sinh ^{n}cx}}={\frac {\cosh cx}{c(n-1)\sinh ^{n-1}cx}}-{\frac {n-2}{n-1}}\int {\frac {dx}{\sinh ^{n-2}cx}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int {\frac {dx}{\sinh ^{n}cx}}={\frac {\cosh cx}{c(n-1)\sinh ^{n-1}cx}}-{\frac {n-2}{n-1}}\int {\frac {dx}{\sinh ^{n-2}cx}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫dxcoshn⁡cx=sinh⁡cxc(n−1)coshn−1⁡cx+n−2n−1∫dxcoshn−2⁡cx(for n≠1){\displaystyle \int {\frac {dx}{\cosh ^{n}cx}}={\frac {\sinh cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\cosh ^{n-2}cx}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int {\frac {dx}{\cosh ^{n}cx}}={\frac {\sinh cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\cosh ^{n-2}cx}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫coshn⁡cxsinhm⁡cxdx=coshn−1⁡cxc(n−m)sinhm−1⁡cx+n−1n−m∫coshn−2⁡cxsinhm⁡cxdx(for m≠n){\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx={\frac {\cosh ^{n-1}cx}{c(n-m)\sinh ^{m-1}cx}}+{\frac {n-1}{n-m}}\int {\frac {\cosh ^{n-2}cx}{\sinh ^{m}cx}}dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}}{\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx={\frac {\cosh ^{n-1}cx}{c(n-m)\sinh ^{m-1}cx}}+{\frac {n-1}{n-m}}\int {\frac {\cosh ^{n-2}cx}{\sinh ^{m}cx}}dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}}
Ayrıca: ∫coshn⁡cxsinhm⁡cxdx=−coshn+1⁡cxc(m−1)sinhm−1⁡cx+n−m+2m−1∫coshn⁡cxsinhm−2⁡cxdx(for m≠1){\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx=-{\frac {\cosh ^{n+1}cx}{c(m-1)\sinh ^{m-1}cx}}+{\frac {n-m+2}{m-1}}\int {\frac {\cosh ^{n}cx}{\sinh ^{m-2}cx}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}{\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx=-{\frac {\cosh ^{n+1}cx}{c(m-1)\sinh ^{m-1}cx}}+{\frac {n-m+2}{m-1}}\int {\frac {\cosh ^{n}cx}{\sinh ^{m-2}cx}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}
Ayrıca: ∫coshn⁡cxsinhm⁡cxdx=−coshn−1⁡cxc(m−1)sinhm−1⁡cx+n−1m−1∫coshn−2⁡cxsinhm−2⁡cxdx(for m≠1){\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx=-{\frac {\cosh ^{n-1}cx}{c(m-1)\sinh ^{m-1}cx}}+{\frac {n-1}{m-1}}\int {\frac {\cosh ^{n-2}cx}{\sinh ^{m-2}cx}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}{\displaystyle \int {\frac {\cosh ^{n}cx}{\sinh ^{m}cx}}dx=-{\frac {\cosh ^{n-1}cx}{c(m-1)\sinh ^{m-1}cx}}+{\frac {n-1}{m-1}}\int {\frac {\cosh ^{n-2}cx}{\sinh ^{m-2}cx}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}
∫sinhm⁡cxcoshn⁡cxdx=sinhm−1⁡cxc(m−n)coshn−1⁡cx+m−1m−n∫sinhm−2⁡cxcoshn⁡cxdx(for m≠n){\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx={\frac {\sinh ^{m-1}cx}{c(m-n)\cosh ^{n-1}cx}}+{\frac {m-1}{m-n}}\int {\frac {\sinh ^{m-2}cx}{\cosh ^{n}cx}}dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}}{\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx={\frac {\sinh ^{m-1}cx}{c(m-n)\cosh ^{n-1}cx}}+{\frac {m-1}{m-n}}\int {\frac {\sinh ^{m-2}cx}{\cosh ^{n}cx}}dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}}
Ayrıca: ∫sinhm⁡cxcoshn⁡cxdx=sinhm+1⁡cxc(n−1)coshn−1⁡cx+m−n+2n−1∫sinhm⁡cxcoshn−2⁡cxdx(for n≠1){\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx={\frac {\sinh ^{m+1}cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {m-n+2}{n-1}}\int {\frac {\sinh ^{m}cx}{\cosh ^{n-2}cx}}dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx={\frac {\sinh ^{m+1}cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {m-n+2}{n-1}}\int {\frac {\sinh ^{m}cx}{\cosh ^{n-2}cx}}dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
Ayrıca: ∫sinhm⁡cxcoshn⁡cxdx=−sinhm−1⁡cxc(n−1)coshn−1⁡cx+m−1n−1∫sinhm−2⁡cxcoshn−2⁡cxdx(for n≠1){\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx=-{\frac {\sinh ^{m-1}cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {m-1}{n-1}}\int {\frac {\sinh ^{m-2}cx}{\cosh ^{n-2}cx}}dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int {\frac {\sinh ^{m}cx}{\cosh ^{n}cx}}dx=-{\frac {\sinh ^{m-1}cx}{c(n-1)\cosh ^{n-1}cx}}+{\frac {m-1}{n-1}}\int {\frac {\sinh ^{m-2}cx}{\cosh ^{n-2}cx}}dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫xsinh⁡cxdx=1cxcosh⁡cx−1c2sinh⁡cx{\displaystyle \int x\sinh cx\,dx={\frac {1}{c}}x\cosh cx-{\frac {1}{c^{2}}}\sinh cx}{\displaystyle \int x\sinh cx\,dx={\frac {1}{c}}x\cosh cx-{\frac {1}{c^{2}}}\sinh cx}
∫xcosh⁡cxdx=1cxsinh⁡cx−1c2cosh⁡cx{\displaystyle \int x\cosh cx\,dx={\frac {1}{c}}x\sinh cx-{\frac {1}{c^{2}}}\cosh cx}{\displaystyle \int x\cosh cx\,dx={\frac {1}{c}}x\sinh cx-{\frac {1}{c^{2}}}\cosh cx}
∫x2cosh⁡cxdx=−2xcosh⁡cxc2+(x2c+2c3)sinh⁡cx{\displaystyle \int x^{2}\cosh cx\,dx=-{\frac {2x\cosh cx}{c^{2}}}+\left({\frac {x^{2}}{c}}+{\frac {2}{c^{3}}}\right)\sinh cx}{\displaystyle \int x^{2}\cosh cx\,dx=-{\frac {2x\cosh cx}{c^{2}}}+\left({\frac {x^{2}}{c}}+{\frac {2}{c^{3}}}\right)\sinh cx}
∫tanh⁡cxdx=1cln⁡|cosh⁡cx|{\displaystyle \int \tanh cx\,dx={\frac {1}{c}}\ln |\cosh cx|}{\displaystyle \int \tanh cx\,dx={\frac {1}{c}}\ln |\cosh cx|}
∫coth⁡cxdx=1cln⁡|sinh⁡cx|{\displaystyle \int \coth cx\,dx={\frac {1}{c}}\ln |\sinh cx|}{\displaystyle \int \coth cx\,dx={\frac {1}{c}}\ln |\sinh cx|}
∫tanhn⁡cxdx=−1c(n−1)tanhn−1⁡cx+∫tanhn−2⁡cxdx(for n≠1){\displaystyle \int \tanh ^{n}cx\,dx=-{\frac {1}{c(n-1)}}\tanh ^{n-1}cx+\int \tanh ^{n-2}cx\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int \tanh ^{n}cx\,dx=-{\frac {1}{c(n-1)}}\tanh ^{n-1}cx+\int \tanh ^{n-2}cx\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫cothn⁡cxdx=−1c(n−1)cothn−1⁡cx+∫cothn−2⁡cxdx(for n≠1){\displaystyle \int \coth ^{n}cx\,dx=-{\frac {1}{c(n-1)}}\coth ^{n-1}cx+\int \coth ^{n-2}cx\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}{\displaystyle \int \coth ^{n}cx\,dx=-{\frac {1}{c(n-1)}}\coth ^{n-1}cx+\int \coth ^{n-2}cx\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫sinh⁡bxsinh⁡cxdx=1b2−c2(bsinh⁡cxcosh⁡bx−ccosh⁡cxsinh⁡bx)(for b2≠c2){\displaystyle \int \sinh bx\sinh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh cx\cosh bx-c\cosh cx\sinh bx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}{\displaystyle \int \sinh bx\sinh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh cx\cosh bx-c\cosh cx\sinh bx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}
∫cosh⁡bxcosh⁡cxdx=1b2−c2(bsinh⁡bxcosh⁡cx−csinh⁡cxcosh⁡bx)(for b2≠c2){\displaystyle \int \cosh bx\cosh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh bx\cosh cx-c\sinh cx\cosh bx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}{\displaystyle \int \cosh bx\cosh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh bx\cosh cx-c\sinh cx\cosh bx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}
∫cosh⁡bxsinh⁡cxdx=1b2−c2(bsinh⁡bxsinh⁡cx−ccosh⁡bxcosh⁡cx)(for b2≠c2){\displaystyle \int \cosh bx\sinh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh bx\sinh cx-c\cosh bx\cosh cx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}{\displaystyle \int \cosh bx\sinh cx\,dx={\frac {1}{b^{2}-c^{2}}}(b\sinh bx\sinh cx-c\cosh bx\cosh cx)\qquad {\mbox{(for }}b^{2}\neq c^{2}{\mbox{)}}}
∫sinh⁡(ax+b)sin⁡(cx+d)dx=aa2+c2cosh⁡(ax+b)sin⁡(cx+d)−ca2+c2sinh⁡(ax+b)cos⁡(cx+d){\displaystyle \int \sinh(ax+b)\sin(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\cosh(ax+b)\sin(cx+d)-{\frac {c}{a^{2}+c^{2}}}\sinh(ax+b)\cos(cx+d)}{\displaystyle \int \sinh(ax+b)\sin(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\cosh(ax+b)\sin(cx+d)-{\frac {c}{a^{2}+c^{2}}}\sinh(ax+b)\cos(cx+d)}
∫sinh⁡(ax+b)cos⁡(cx+d)dx=aa2+c2cosh⁡(ax+b)cos⁡(cx+d)+ca2+c2sinh⁡(ax+b)sin⁡(cx+d){\displaystyle \int \sinh(ax+b)\cos(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)+{\frac {c}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)}{\displaystyle \int \sinh(ax+b)\cos(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)+{\frac {c}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)}
∫cosh⁡(ax+b)sin⁡(cx+d)dx=aa2+c2sinh⁡(ax+b)sin⁡(cx+d)−ca2+c2cosh⁡(ax+b)cos⁡(cx+d){\displaystyle \int \cosh(ax+b)\sin(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)-{\frac {c}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)}{\displaystyle \int \cosh(ax+b)\sin(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)-{\frac {c}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)}
∫cosh⁡(ax+b)cos⁡(cx+d)dx=aa2+c2sinh⁡(ax+b)cos⁡(cx+d)+ca2+c2cosh⁡(ax+b)sin⁡(cx+d){\displaystyle \int \cosh(ax+b)\cos(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\sinh(ax+b)\cos(cx+d)+{\frac {c}{a^{2}+c^{2}}}\cosh(ax+b)\sin(cx+d)}{\displaystyle \int \cosh(ax+b)\cos(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\sinh(ax+b)\cos(cx+d)+{\frac {c}{a^{2}+c^{2}}}\cosh(ax+b)\sin(cx+d)}

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Asagidaki liste integrallerini icermektedir Integral fonksiyonlarinin tum bir listesi icin lutfen Integral tablosu sayfasina bakiniz c sabiti sifirdan farkli varsayilmistir sinh cxdx 1ccosh cx displaystyle int sinh cx dx frac 1 c cosh cx cosh cxdx 1csinh cx displaystyle int cosh cx dx frac 1 c sinh cx sinh2 cxdx 14csinh 2cx x2 displaystyle int sinh 2 cx dx frac 1 4c sinh 2cx frac x 2 cosh2 cxdx 14csinh 2cx x2 displaystyle int cosh 2 cx dx frac 1 4c sinh 2cx frac x 2 tanh2 cxdx x tanh cxc displaystyle int tanh 2 cx dx x frac tanh cx c sinhn cxdx 1cnsinhn 1 cxcosh cx n 1n sinhn 2 cxdx for n gt 0 displaystyle int sinh n cx dx frac 1 cn sinh n 1 cx cosh cx frac n 1 n int sinh n 2 cx dx qquad mbox for n gt 0 mbox Ayrica sinhn cxdx 1c n 1 sinhn 1 cxcosh cx n 2n 1 sinhn 2 cxdx for n lt 0 n 1 displaystyle int sinh n cx dx frac 1 c n 1 sinh n 1 cx cosh cx frac n 2 n 1 int sinh n 2 cx dx qquad mbox for n lt 0 mbox n neq 1 mbox coshn cxdx 1cnsinh cxcoshn 1 cx n 1n coshn 2 cxdx for n gt 0 displaystyle int cosh n cx dx frac 1 cn sinh cx cosh n 1 cx frac n 1 n int cosh n 2 cx dx qquad mbox for n gt 0 mbox Ayrica coshn cxdx 1c n 1 sinh cxcoshn 1 cx n 2n 1 coshn 2 cxdx for n lt 0 n 1 displaystyle int cosh n cx dx frac 1 c n 1 sinh cx cosh n 1 cx frac n 2 n 1 int cosh n 2 cx dx qquad mbox for n lt 0 mbox n neq 1 mbox dxsinh cx 1cln tanh cx2 displaystyle int frac dx sinh cx frac 1 c ln left tanh frac cx 2 right Ayrica dxsinh cx 1cln cosh cx 1sinh cx displaystyle int frac dx sinh cx frac 1 c ln left frac cosh cx 1 sinh cx right Ayrica dxsinh cx 1cln sinh cxcosh cx 1 displaystyle int frac dx sinh cx frac 1 c ln left frac sinh cx cosh cx 1 right Ayrica dxsinh cx 1cln cosh cx 1cosh cx 1 displaystyle int frac dx sinh cx frac 1 c ln left frac cosh cx 1 cosh cx 1 right dxcosh cx 2carctan ecx displaystyle int frac dx cosh cx frac 2 c arctan e cx dxsinhn cx cosh cxc n 1 sinhn 1 cx n 2n 1 dxsinhn 2 cx for n 1 displaystyle int frac dx sinh n cx frac cosh cx c n 1 sinh n 1 cx frac n 2 n 1 int frac dx sinh n 2 cx qquad mbox for n neq 1 mbox dxcoshn cx sinh cxc n 1 coshn 1 cx n 2n 1 dxcoshn 2 cx for n 1 displaystyle int frac dx cosh n cx frac sinh cx c n 1 cosh n 1 cx frac n 2 n 1 int frac dx cosh n 2 cx qquad mbox for n neq 1 mbox coshn cxsinhm cxdx coshn 1 cxc n m sinhm 1 cx n 1n m coshn 2 cxsinhm cxdx for m n displaystyle int frac cosh n cx sinh m cx dx frac cosh n 1 cx c n m sinh m 1 cx frac n 1 n m int frac cosh n 2 cx sinh m cx dx qquad mbox for m neq n mbox Ayrica coshn cxsinhm cxdx coshn 1 cxc m 1 sinhm 1 cx n m 2m 1 coshn cxsinhm 2 cxdx for m 1 displaystyle int frac cosh n cx sinh m cx dx frac cosh n 1 cx c m 1 sinh m 1 cx frac n m 2 m 1 int frac cosh n cx sinh m 2 cx dx qquad mbox for m neq 1 mbox Ayrica coshn cxsinhm cxdx coshn 1 cxc m 1 sinhm 1 cx n 1m 1 coshn 2 cxsinhm 2 cxdx for m 1 displaystyle int frac cosh n cx sinh m cx dx frac cosh n 1 cx c m 1 sinh m 1 cx frac n 1 m 1 int frac cosh n 2 cx sinh m 2 cx dx qquad mbox for m neq 1 mbox sinhm cxcoshn cxdx sinhm 1 cxc m n coshn 1 cx m 1m n sinhm 2 cxcoshn cxdx for m n displaystyle int frac sinh m cx cosh n cx dx frac sinh m 1 cx c m n cosh n 1 cx frac m 1 m n int frac sinh m 2 cx cosh n cx dx qquad mbox for m neq n mbox Ayrica sinhm cxcoshn cxdx sinhm 1 cxc n 1 coshn 1 cx m n 2n 1 sinhm cxcoshn 2 cxdx for n 1 displaystyle int frac sinh m cx cosh n cx dx frac sinh m 1 cx c n 1 cosh n 1 cx frac m n 2 n 1 int frac sinh m cx cosh n 2 cx dx qquad mbox for n neq 1 mbox Ayrica sinhm cxcoshn cxdx sinhm 1 cxc n 1 coshn 1 cx m 1n 1 sinhm 2 cxcoshn 2 cxdx for n 1 displaystyle int frac sinh m cx cosh n cx dx frac sinh m 1 cx c n 1 cosh n 1 cx frac m 1 n 1 int frac sinh m 2 cx cosh n 2 cx dx qquad mbox for n neq 1 mbox xsinh cxdx 1cxcosh cx 1c2sinh cx displaystyle int x sinh cx dx frac 1 c x cosh cx frac 1 c 2 sinh cx xcosh cxdx 1cxsinh cx 1c2cosh cx displaystyle int x cosh cx dx frac 1 c x sinh cx frac 1 c 2 cosh cx x2cosh cxdx 2xcosh cxc2 x2c 2c3 sinh cx displaystyle int x 2 cosh cx dx frac 2x cosh cx c 2 left frac x 2 c frac 2 c 3 right sinh cx tanh cxdx 1cln cosh cx displaystyle int tanh cx dx frac 1 c ln cosh cx coth cxdx 1cln sinh cx displaystyle int coth cx dx frac 1 c ln sinh cx tanhn cxdx 1c n 1 tanhn 1 cx tanhn 2 cxdx for n 1 displaystyle int tanh n cx dx frac 1 c n 1 tanh n 1 cx int tanh n 2 cx dx qquad mbox for n neq 1 mbox cothn cxdx 1c n 1 cothn 1 cx cothn 2 cxdx for n 1 displaystyle int coth n cx dx frac 1 c n 1 coth n 1 cx int coth n 2 cx dx qquad mbox for n neq 1 mbox sinh bxsinh cxdx 1b2 c2 bsinh cxcosh bx ccosh cxsinh bx for b2 c2 displaystyle int sinh bx sinh cx dx frac 1 b 2 c 2 b sinh cx cosh bx c cosh cx sinh bx qquad mbox for b 2 neq c 2 mbox cosh bxcosh cxdx 1b2 c2 bsinh bxcosh cx csinh cxcosh bx for b2 c2 displaystyle int cosh bx cosh cx dx frac 1 b 2 c 2 b sinh bx cosh cx c sinh cx cosh bx qquad mbox for b 2 neq c 2 mbox cosh bxsinh cxdx 1b2 c2 bsinh bxsinh cx ccosh bxcosh cx for b2 c2 displaystyle int cosh bx sinh cx dx frac 1 b 2 c 2 b sinh bx sinh cx c cosh bx cosh cx qquad mbox for b 2 neq c 2 mbox sinh ax b sin cx d dx aa2 c2cosh ax b sin cx d ca2 c2sinh ax b cos cx d displaystyle int sinh ax b sin cx d dx frac a a 2 c 2 cosh ax b sin cx d frac c a 2 c 2 sinh ax b cos cx d sinh ax b cos cx d dx aa2 c2cosh ax b cos cx d ca2 c2sinh ax b sin cx d displaystyle int sinh ax b cos cx d dx frac a a 2 c 2 cosh ax b cos cx d frac c a 2 c 2 sinh ax b sin cx d cosh ax b sin cx d dx aa2 c2sinh ax b sin cx d ca2 c2cosh ax b cos cx d displaystyle int cosh ax b sin cx d dx frac a a 2 c 2 sinh ax b sin cx d frac c a 2 c 2 cosh ax b cos cx d cosh ax b cos cx d dx aa2 c2sinh ax b cos cx d ca2 c2cosh ax b sin cx d displaystyle int cosh ax b cos cx d dx frac a a 2 c 2 sinh ax b cos cx d frac c a 2 c 2 cosh ax b sin cx d

Yayın tarihi: Temmuz 24, 2024, 21:29 pm
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