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受欢迎的微积分 >

integral of 3/((xln^2(3x)))

解答

\int \frac{3}{( x ln ^{2} ( 3 x ) )} d x

解答

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

求解步骤

\int \frac{3}{x ln ^{2} ( 3 x )} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{x ln ^{2} ( 3 x )} d x

使用换元积分法

= 3 \cdot \int \frac{1}{u ln ^{2} ( u )} d u

使用换元积分法

= 3 \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 3 (- \frac{1}{v})

代回

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

化简

3 (- \frac{1}{ln ( 3 x )}) : - \frac{3}{ln ( 3 x )}

= - \frac{3}{ln ( 3 x )}

解答补常数

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

作图

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