integral of x(ln(x^2))

解

\int x (ln (x^{2})) d x

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

解答ステップ

\int x ln (x^{2}) d x

部分積分を適用する

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

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

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

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

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

定数を解答に追加する

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