integral of xsinh(2x)

解答

\int x sinh (2 x) d x

\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x) + C

求解步骤

\int x sinh (2 x) d x

使用分布积分法

= \frac{1}{2} x cosh (2 x) - \int \frac{1}{2} cosh (2 x) d x

\int \frac{1}{2} cosh (2 x) d x = \frac{1}{4} sinh (2 x)

= \frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x)

解答补常数

= \frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x) + C

d er i v a t i v e 15 e^{x}

\frac{d}{d x} (- \frac{1}{3 5 7 cos ( 2 x )})

\frac{d}{d x} ((5 x + 3)^{4})

\frac{d}{d x} ((arctan (7 x))^{2})

x \to a lim (\frac{3 x - 3 a}{x ^{2} - a ^{2}})