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Asagidaki liste integrallerini vermektedir ax b ndx ax b n 1a n 1 n 1 for displaystyle int ax b n dx frac ax b n 1 a n 1 qquad text n neq 1 text for dxax b 1aln ax b displaystyle int frac dx ax b frac 1 a ln left ax b right x ax b ndx a n 1 x ba2 n 1 n 2 ax b n 1 for n 2 1 displaystyle int x ax b n dx frac a n 1 x b a 2 n 1 n 2 ax b n 1 qquad text for n not in 2 1 text xax bdx xa ba2ln ax b displaystyle int frac x ax b dx frac x a frac b a 2 ln left ax b right x ax b 2dx ba2 ax b 1a2ln ax b displaystyle int frac x ax b 2 dx frac b a 2 ax b frac 1 a 2 ln left ax b right x ax b ndx a 1 n x ba2 n 1 n 2 ax b n 1 for n 1 2 displaystyle int frac x ax b n dx frac a 1 n x b a 2 n 1 n 2 ax b n 1 qquad text for n not in 1 2 text x2ax bdx 1a3 ax b 22 2b ax b b2ln ax b displaystyle int frac x 2 ax b dx frac 1 a 3 left frac ax b 2 2 2b ax b b 2 ln left ax b right right x2 ax b 2dx 1a3 ax b 2bln ax b b2ax b displaystyle int frac x 2 ax b 2 dx frac 1 a 3 left ax b 2b ln left ax b right frac b 2 ax b right x2 ax b 3dx 1a3 ln ax b 2bax b b22 ax b 2 displaystyle int frac x 2 ax b 3 dx frac 1 a 3 left ln left ax b right frac 2b ax b frac b 2 2 ax b 2 right x2 ax b ndx 1a3 1 n 3 ax b n 3 2b n 2 ax b n 2 b2 n 1 ax b n 1 for n 1 2 3 displaystyle int frac x 2 ax b n dx frac 1 a 3 left frac 1 n 3 ax b n 3 frac 2b n 2 ax b n 2 frac b 2 n 1 ax b n 1 right qquad text for n not in 1 2 3 text dxx ax b 1bln ax bx displaystyle int frac dx x ax b frac 1 b ln left frac ax b x right dxx2 ax b 1bx ab2ln ax bx displaystyle int frac dx x 2 ax b frac 1 bx frac a b 2 ln left frac ax b x right dxx2 ax b 2 a 1b2 ax b 1ab2x 2b3ln ax bx displaystyle int frac dx x 2 ax b 2 a left frac 1 b 2 ax b frac 1 ab 2 x frac 2 b 3 ln left frac ax b x right right dxx2 a2 1aarctan xa displaystyle int frac dx x 2 a 2 frac 1 a arctan frac x a dxx2 a2 1aartanh xa 12aln a xa x for x lt a displaystyle int frac dx x 2 a 2 frac 1 a operatorname artanh frac x a frac 1 2a ln frac a x a x qquad text for x lt a text dxx2 a2 1aarcoth xa 12aln x ax a for x gt a displaystyle int frac dx x 2 a 2 frac 1 a operatorname arcoth frac x a frac 1 2a ln frac x a x a qquad text for x gt a text dxax2 bx c 24ac b2arctan 2ax b4ac b2 for 4ac b2 gt 0 displaystyle int frac dx ax 2 bx c frac 2 sqrt 4ac b 2 arctan frac 2ax b sqrt 4ac b 2 qquad text for 4ac b 2 gt 0 text dxax2 bx c 2b2 4acartanh 2ax bb2 4ac 1b2 4acln 2ax b b2 4ac2ax b b2 4ac for 4ac b2 lt 0 displaystyle int frac dx ax 2 bx c frac 2 sqrt b 2 4ac operatorname artanh frac 2ax b sqrt b 2 4ac frac 1 sqrt b 2 4ac ln left frac 2ax b sqrt b 2 4ac 2ax b sqrt b 2 4ac right qquad text for 4ac b 2 lt 0 text dxax2 bx c 22ax b for 4ac b2 0 displaystyle int frac dx ax 2 bx c frac 2 2ax b qquad text for 4ac b 2 0 text xax2 bx cdx 12aln ax2 bx c b2a dxax2 bx c displaystyle int frac x ax 2 bx c dx frac 1 2a ln left ax 2 bx c right frac b 2a int frac dx ax 2 bx c mx nax2 bx cdx m2aln ax2 bx c 2an bma4ac b2arctan 2ax b4ac b2 for 4ac b2 gt 0 displaystyle int frac mx n ax 2 bx c dx frac m 2a ln left ax 2 bx c right frac 2an bm a sqrt 4ac b 2 arctan frac 2ax b sqrt 4ac b 2 qquad text for 4ac b 2 gt 0 text mx nax2 bx cdx m2aln ax2 bx c 2an bmab2 4acartanh 2ax bb2 4ac for 4ac b2 lt 0 displaystyle int frac mx n ax 2 bx c dx frac m 2a ln left ax 2 bx c right frac 2an bm a sqrt b 2 4ac operatorname artanh frac 2ax b sqrt b 2 4ac qquad text for 4ac b 2 lt 0 text mx nax2 bx cdx m2aln ax2 bx c 2an bma 2ax b For 4ac b2 0 displaystyle int frac mx n ax 2 bx c dx frac m 2a ln left ax 2 bx c right frac 2an bm a 2ax b qquad text For 4ac b 2 0 text dx ax2 bx c n 2ax b n 1 4ac b2 ax2 bx c n 1 2n 3 2a n 1 4ac b2 dx ax2 bx c n 1 displaystyle int frac dx ax 2 bx c n frac 2ax b n 1 4ac b 2 ax 2 bx c n 1 frac 2n 3 2a n 1 4ac b 2 int frac dx ax 2 bx c n 1 x ax2 bx c ndx bx 2c n 1 4ac b2 ax2 bx c n 1 b 2n 3 n 1 4ac b2 dx ax2 bx c n 1 displaystyle int frac x ax 2 bx c n dx frac bx 2c n 1 4ac b 2 ax 2 bx c n 1 frac b 2n 3 n 1 4ac b 2 int frac dx ax 2 bx c n 1 dxx ax2 bx c 12cln x2ax2 bx c b2c dxax2 bx c displaystyle int frac dx x ax 2 bx c frac 1 2c ln left frac x 2 ax 2 bx c right frac b 2c int frac dx ax 2 bx c x2r y2r r displaystyle int frac x 2 r frac y 2 r r x y n displaystyle int x y n Ayrica bakinizIntegral tablosu