双曲函数积分表, 此條目没有列出任何参考或来源, 2017年12月26日, 維基百科所有的內容都應該可供查證, 请协助補充可靠来源以改善这篇条目, 无法查证的內容可能會因為異議提出而被移除, 以下是部份双曲函数的积分表, 书写时省略了不定积分结果中都含有的任意常数cn, sinh, cosh, displaystyle, sinh, frac, cosh, cosh, sinh, displaystyle, cosh, frac, sinh, sinh, sinh, displaystyle, sinh, frac. 此條目没有列出任何参考或来源 2017年12月26日 維基百科所有的內容都應該可供查證 请协助補充可靠来源以改善这篇条目 无法查证的內容可能會因為異議提出而被移除 以下是部份双曲函数的积分表 书写时省略了不定积分结果中都含有的任意常数Cn sinh c x d x 1 c cosh c x displaystyle int sinh cx dx frac 1 c cosh cx cosh c x d x 1 c sinh c x displaystyle int cosh cx dx frac 1 c sinh cx sinh 2 c x d x 1 4 c sinh 2 c x x 2 displaystyle int sinh 2 cx dx frac 1 4c sinh 2cx frac x 2 cosh 2 c x d x 1 4 c sinh 2 c x x 2 displaystyle int cosh 2 cx dx frac 1 4c sinh 2cx frac x 2 sinh n c x d x 1 c n sinh n 1 c x cosh c x n 1 n sinh n 2 c x d x 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 sinh n c x d x 1 c n 1 sinh n 1 c x cosh c x n 2 n 1 sinh n 2 c x d x 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 cosh n c x d x 1 c n sinh c x cosh n 1 c x n 1 n cosh n 2 c x d x 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 cosh n c x d x 1 c n 1 sinh c x cosh n 1 c x n 2 n 1 cosh n 2 c x d x 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 d x sinh c x 1 c ln tanh c x 2 displaystyle int frac dx sinh cx frac 1 c ln left tanh frac cx 2 right d x sinh c x 1 c ln cosh c x 1 sinh c x displaystyle int frac dx sinh cx frac 1 c ln left frac cosh cx 1 sinh cx right d x sinh c x 1 c ln sinh c x cosh c x 1 displaystyle int frac dx sinh cx frac 1 c ln left frac sinh cx cosh cx 1 right d x sinh c x 1 2 c ln cosh c x 1 cosh c x 1 displaystyle int frac dx sinh cx frac 1 2c ln left frac cosh cx 1 cosh cx 1 right d x cosh c x 2 c arctan e c x displaystyle int frac dx cosh cx frac 2 c arctan e cx d x sinh n c x cosh c x c n 1 sinh n 1 c x n 2 n 1 d x sinh n 2 c x 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 d x cosh n c x sinh c x c n 1 cosh n 1 c x n 2 n 1 d x cosh n 2 c x 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 cosh n c x sinh m c x d x cosh n 1 c x c n m sinh m 1 c x n 1 n m cosh n 2 c x sinh m c x d x 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 cosh n c x sinh m c x d x cosh n 1 c x c m 1 sinh m 1 c x n m 2 m 1 cosh n c x sinh m 2 c x d x 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 cosh n c x sinh m c x d x cosh n 1 c x c m 1 sinh m 1 c x n 1 m 1 cosh n 2 c x sinh m 2 c x d x 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 sinh m c x cosh n c x d x sinh m 1 c x c m n cosh n 1 c x m 1 m n sinh m 2 c x cosh n c x d x 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 sinh m c x cosh n c x d x sinh m 1 c x c n 1 cosh n 1 c x m n 2 n 1 sinh m c x cosh n 2 c x d x 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 sinh m c x cosh n c x d x sinh m 1 c x c n 1 cosh n 1 c x m 1 n 1 sinh m 2 c x cosh n 2 c x d x 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 x sinh c x d x 1 c x cosh c x 1 c 2 sinh c x displaystyle int x sinh cx dx frac 1 c x cosh cx frac 1 c 2 sinh cx x cosh c x d x 1 c x sinh c x 1 c 2 cosh c x displaystyle int x cosh cx dx frac 1 c x sinh cx frac 1 c 2 cosh cx tanh c x d x 1 c ln cosh c x displaystyle int tanh cx dx frac 1 c ln cosh cx coth c x d x 1 c ln sinh c x displaystyle int coth cx dx frac 1 c ln sinh cx tanh n c x d x 1 c n 1 tanh n 1 c x tanh n 2 c x d x 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 coth n c x d x 1 c n 1 coth n 1 c x coth n 2 c x d x 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 b x sinh c x d x 1 b 2 c 2 b sinh c x cosh b x c cosh c x sinh b x for b 2 c 2 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 b x cosh c x d x 1 b 2 c 2 b sinh b x cosh c x c sinh c x cosh b x for b 2 c 2 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 b x sinh c x d x 1 b 2 c 2 b sinh b x sinh c x c cosh b x cosh c x for b 2 c 2 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 a x b sin c x d d x a a 2 c 2 cosh a x b sin c x d c a 2 c 2 sinh a x b cos c x 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 a x b cos c x d d x a a 2 c 2 cosh a x b cos c x d c a 2 c 2 sinh a x b sin c x 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 a x b sin c x d d x a a 2 c 2 sinh a x b sin c x d c a 2 c 2 cosh a x b cos c x 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 a x b cos c x d d x a a 2 c 2 sinh a x b cos c x d c a 2 c 2 cosh a x b sin c x 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 取自 https zh wikipedia org w index php title 双曲函数积分表 amp oldid 77062253, 维基百科,wiki,书籍,书籍,图书馆,