integral of 1/(sqrt(a-x))

解答

\int \frac{1}{a - x} d x

- 2 a - x + C

求解步骤

\int \frac{1}{a - x} d x

使用换元积分法

= \int - \frac{1}{u} d u

提出常数:

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

= - \int \frac{1}{u} d u

使用幂法则

= - 2 u^{\frac{1}{2}}

u = a - x

代回

= - 2 (a - x)^{\frac{1}{2}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

= - 2 a - x

解答补常数

= - 2 a - x + C

\int (- 16 tan (x) cos (x)) d x

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