integral of x(x-10)^{10}

解

\int x (x - 10)^{10} d x

\frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12} + C

解答ステップ

\int x (x - 10)^{10} d x

部分積分を適用する

= \frac{1}{11} x (x - 10)^{11} - \int \frac{1}{11} (x - 10)^{11} d x

\int \frac{1}{11} (x - 10)^{11} d x = \frac{1}{132} (x - 10)^{12}

= \frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12}

定数を解答に追加する

= \frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12} + C