integral of (100)/(sqrt(100-x^2))

解答

\int \frac{100}{100 - x ^{2}} d x

100 arcsin (\frac{1}{10} x) + C

求解步骤

\int \frac{100}{100 - x ^{2}} d x

提出常数:

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

= 100 \cdot \int \frac{1}{100 - x ^{2}} d x

使用三角换元法

= 100 \cdot \int 1 d u

常数积分:

\int a d x = a x

= 100 \cdot 1 \cdot u

u = arcsin (\frac{1}{10} x)

代回

= 100 \cdot 1 \cdot arcsin (\frac{1}{10} x)

化简

= 100 arcsin (\frac{1}{10} x)

解答补常数

= 100 arcsin (\frac{1}{10} x) + C

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