integral of y^2sinh(5y)

解答

\int y^{2} sinh (5 y) d y

\frac{1}{5} y^{2} cosh (5 y) - \frac{2}{5} (\frac{1}{5} y sinh (5 y) - \frac{1}{25} cosh (5 y)) + C

求解步骤

\int y^{2} sinh (5 y) d y

使用分布积分法

= \frac{1}{5} y^{2} cosh (5 y) - \int \frac{2}{5} y cosh (5 y) d y

\int \frac{2}{5} y cosh (5 y) d y = \frac{2}{5} (\frac{1}{5} y sinh (5 y) - \frac{1}{25} cosh (5 y))

= \frac{1}{5} y^{2} cosh (5 y) - \frac{2}{5} (\frac{1}{5} y sinh (5 y) - \frac{1}{25} cosh (5 y))

解答补常数

= \frac{1}{5} y^{2} cosh (5 y) - \frac{2}{5} (\frac{1}{5} y sinh (5 y) - \frac{1}{25} cosh (5 y)) + C

\int_{0}^{1} \int_{0}^{x} \frac{4 - 2 y}{( 1 + x ) ^{2}} d y d x

\int_{0}^{\frac{π}{24}} cos (6 x) d x

\frac{\partial}{\partial z} (3 y e^{- z})

\frac{d y}{d x} = (\frac{( 2 y + 3 )}{4 x + 5})^{2}

\frac{d}{d x} (ln (\frac{3 x + 1}{x ^{2} - 2}))