integral of xln(x^5)

解

\int x ln (x^{5}) d x

\frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4} + C

解答ステップ

\int x ln (x^{5}) d x

部分積分を適用する

= \frac{1}{2} x^{2} ln (x^{5}) - \int \frac{5 x}{2} d x

\int \frac{5 x}{2} d x = \frac{5 x ^{2}}{4}

= \frac{1}{2} x^{2} ln (x^{5}) - \frac{5 x ^{2}}{4}

\frac{1}{2} x^{2} ln (x^{5}) = \frac{5}{2} x^{2} ln (x)

= \frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4}

定数を解答に追加する

= \frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4} + C