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Hàm_hyperbolic Nguyên hàmXem thêm: Danh sách tích phân với hàm hyperbolic
∫ sinh a x d x = a − 1 cosh a x + C {\displaystyle \int \sinh ax\,dx=a^{-1}\cosh ax+C} ∫ cosh a x d x = a − 1 sinh a x + C {\displaystyle \int \cosh ax\,dx=a^{-1}\sinh ax+C} ∫ tanh a x d x = a − 1 ln ( cosh a x ) + C {\displaystyle \int \tanh ax\,dx=a^{-1}\ln(\cosh ax)+C} ∫ coth a x d x = a − 1 ln ( sinh a x ) + C {\displaystyle \int \coth ax\,dx=a^{-1}\ln(\sinh ax)+C} ∫ d u a 2 + u 2 = sinh − 1 ( u a ) + C {\displaystyle \int {\frac {du}{\sqrt {a^{2}+u^{2}}}}=\sinh ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u u 2 − a 2 = cosh − 1 ( u a ) + C {\displaystyle \int {\frac {du}{\sqrt {u^{2}-a^{2}}}}=\cosh ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u a 2 − u 2 = a − 1 tanh − 1 ( u a ) + C ; u 2 < a 2 {\displaystyle \int {\frac {du}{a^{2}-u^{2}}}=a^{-1}\tanh ^{-1}\left({\frac {u}{a}}\right)+C;u^{2}<a^{2}} ∫ d u a 2 − u 2 = a − 1 coth − 1 ( u a ) + C ; u 2 > a 2 {\displaystyle \int {\frac {du}{a^{2}-u^{2}}}=a^{-1}\coth ^{-1}\left({\frac {u}{a}}\right)+C;u^{2}>a^{2}} ∫ d u u a 2 − u 2 = − a − 1 sech − 1 ( u a ) + C {\displaystyle \int {\frac {du}{u{\sqrt {a^{2}-u^{2}}}}}=-a^{-1}\operatorname {sech} ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u u a 2 + u 2 = − a − 1 csch − 1 | u a | + C {\displaystyle \int {\frac {du}{u{\sqrt {a^{2}+u^{2}}}}}=-a^{-1}\operatorname {csch} ^{-1}\left|{\frac {u}{a}}\right|+C}với C là hằng số tích phân.
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Hàm_hyperbolic Nguyên hàmLiên quan
Hàm hyperbol Hàm Hưng Hàm hyperbolic ngược Hàm hợp Hàm hằng Hàm Huy Hàm hủy (lập trình máy tính) Hàm Hiệp Hàm hermite Hàm hóaTài liệu tham khảo
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