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受欢迎的微积分 >

integral of (csc^2(sqrt(x)))/(2sqrt(x))

解答

\int \frac{csc ^{2} ( x )}{2 x} d x

解答

- cot (x) + C

求解步骤

\int \frac{csc ^{2} ( x )}{2 x} d x

提出常数:

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

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

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{2} \cdot 2 (- cot (u))

u = x

代回

= \frac{1}{2} \cdot 2 (- cot (x))

化简

\frac{1}{2} \cdot 2 (- cot (x)) : - cot (x)

= - cot (x)

解答补常数

= - cot (x) + C

作图

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