integral of ln(2x^2)

解答

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

x (ln (2) + 2 ln (x)) - 2 x + C

求解步骤

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

使用分布积分法

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

\int 2 d x = 2 x

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

化简

ln (2 x^{2}) : 2 ln (x) + ln (2)

= x (ln (2) + 2 ln (x)) - 2 x

解答补常数

= x (ln (2) + 2 ln (x)) - 2 x + C

\int \frac{a ^{2} + x ^{2}}{x} d x

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