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受欢迎的微积分 >

integral of 1/(sqrt(-x^2-6x+16))

解答

\int \frac{1}{- x ^{2} - 6 x + 16} d x

解答

arcsin (\frac{1}{5} (x + 3)) + C

求解步骤

\int \frac{1}{- x ^{2} - 6 x + 16} d x

对

- x^{2} - 6 x + 16

配方:

- (x + 3)^{2} + 25

= \int \frac{1}{- ( x + 3 ) ^{2} + 25} d x

使用换元积分法

= \int \frac{1}{- u ^{2} + 25} 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}{5} (x + 3))

化简

= arcsin (\frac{1}{5} (x + 3))

解答补常数

= arcsin (\frac{1}{5} (x + 3)) + C

作图

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