What is the integral of y^2sinh(5y) ?

The integral of y^2sinh(5y) is 1/5 y^2cosh(5y)-2/5 (1/5 ysinh(5y)-1/25 cosh(5y))+C

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integral of y^2sinh(5y)

\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

Solution steps

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

Apply Integration By Parts

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

= \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))

Add a constant to the solution

= \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

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\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}))

What is the integral of y^2sinh(5y) ?
The integral of y^2sinh(5y) is 1/5 y^2cosh(5y)-2/5 (1/5 ysinh(5y)-1/25 cosh(5y))+C