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受欢迎的微积分 >

integral of-9cot(x)ln(sin(x))

解答

\int - 9 cot (x) ln (sin (x)) d x

解答

- \frac{9}{2} ln^{2} (sin (x)) + C

求解步骤

\int - 9 cot (x) ln (sin (x)) d x

提出常数:

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

= - 9 \cdot \int cot (x) ln (sin (x)) d x

使用三角恒等式改写

= - 9 \cdot \int cos (x) ln (sin (x)) csc (x) d x

使用换元积分法

= - 9 \cdot \int \frac{ln ( u )}{u} d u

使用换元积分法

= - 9 \cdot \int v d v

使用幂法则

= - 9 \cdot \frac{v ^{2}}{2}

代回

= - 9 \cdot \frac{ln ^{2} ( sin ( x ) )}{2}

化简

- 9 \cdot \frac{ln ^{2} ( sin ( x ) )}{2} : - \frac{9}{2} ln^{2} (sin (x))

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

解答补常数

= - \frac{9}{2} ln^{2} (sin (x)) + C

作图

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