integral of ln(9sqrt(x))

解答

\int ln (9 x) d x

x (2 ln (3) + \frac{1}{2} ln (x)) - \frac{1}{2} x + C

求解步骤

\int ln (9 x) d x

使用分布积分法

= x ln (9 x) - \int \frac{1}{2} d x

\int \frac{1}{2} d x = \frac{1}{2} x

= x ln (9 x) - \frac{1}{2} x

x ln (9 x) = x (2 ln (3) + \frac{1}{2} ln (x))

= x (2 ln (3) + \frac{1}{2} ln (x)) - \frac{1}{2} x

解答补常数

= x (2 ln (3) + \frac{1}{2} ln (x)) - \frac{1}{2} x + C

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