integral of x^2sin(7x)

解

\int x^{2} sin (7 x) d x

- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)) + C

解答ステップ

\int x^{2} sin (7 x) d x

部分積分を適用する

= - \frac{1}{7} x^{2} cos (7 x) - \int - \frac{2}{7} x cos (7 x) d x

\int - \frac{2}{7} x cos (7 x) d x = - \frac{2}{343} (7 x sin (7 x) + cos (7 x))

= - \frac{1}{7} x^{2} cos (7 x) - (- \frac{2}{343} (7 x sin (7 x) + cos (7 x)))

簡素化

= - \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x))

定数を解答に追加する

= - \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)) + C