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受欢迎的微积分 >

integral of 2/(sqrt(36-25y^2))

解答

\int \frac{2}{36 - 25 y ^{2}} d y

解答

\frac{2}{5} arcsin (\frac{5}{6} y) + C

求解步骤

\int \frac{2}{36 - 25 y ^{2}} d y

提出常数:

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

= 2 \cdot \int \frac{1}{36 - 25 y ^{2}} d y

使用三角换元法

= 2 \cdot \int \frac{1}{5} d u

提出常数:

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

= 2 \cdot \frac{1}{5} \cdot \int 1 d u

常数积分:

\int a d x = a x

= 2 \cdot \frac{1}{5} \cdot 1 \cdot u

u = arcsin (\frac{5}{6} y)

代回

= 2 \cdot \frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{6} y)

化简

2 \cdot \frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{6} y) : \frac{2}{5} arcsin (\frac{5}{6} y)

= \frac{2}{5} arcsin (\frac{5}{6} y)

解答补常数

= \frac{2}{5} arcsin (\frac{5}{6} y) + C

作图

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