integral of (ln(16x))^2

解答

\int (ln (16 x))^{2} d x

x ln^{2} (16 x) - 2 (x ln (16 x) - x) + C

求解步骤

\int (ln (16 x))^{2} d x

使用分布积分法

= x ln^{2} (16 x) - \int 2 ln (16 x) d x

\int 2 ln (16 x) d x = 2 (x ln (16 x) - x)

= x ln^{2} (16 x) - 2 (x ln (16 x) - x)

解答补常数

= x ln^{2} (16 x) - 2 (x ln (16 x) - x) + C

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