integral of y^2sinh(5y)

解

\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

解答ステップ

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

部分積分を適用する

= \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))

定数を解答に追加する

= \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