integral of 1/(sqrt(9-(x+2)^2))

解答

\int \frac{1}{9 - ( x + 2 ) ^{2}} d x

arcsin (\frac{1}{3} (x + 2)) + C

求解步骤

\int \frac{1}{9 - ( x + 2 ) ^{2}} d x

使用换元积分法

= \int \frac{1}{9 - u ^{2}} d u

使用三角换元法

= \int 1 d v

常数积分:

\int a d x = a x

= 1 \cdot v

代回

= 1 \cdot arcsin (\frac{1}{3} (x + 2))

化简

= arcsin (\frac{1}{3} (x + 2))

解答补常数

= arcsin (\frac{1}{3} (x + 2)) + C

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