integral of 1/(sqrt((25-y^2)-x^2))

解答

\int \frac{1}{( 25 - y ^{2} ) - x ^{2}} d x

arcsin (\frac{x}{25 - y ^{2}}) + C

求解步骤

\int \frac{1}{25 - y ^{2} - x ^{2}} d x

使用三角换元法

= \int 1 d u

常数积分:

\int a d x = a x

= 1 \cdot u

u = arcsin (\frac{1}{25 - y ^{2}} x)

代回

= 1 \cdot arcsin (\frac{1}{25 - y ^{2}} x)

化简

1 \cdot arcsin (\frac{1}{25 - y ^{2}} x) : arcsin (\frac{x}{25 - y ^{2}})

= arcsin (\frac{x}{25 - y ^{2}})

解答补常数

= arcsin (\frac{x}{25 - y ^{2}}) + C

l a pl a ce t r an s f or m sin (2 t) + 2 cos (2 t) + e^{- t} sin (2 t)

y^{^{'}} = 3 y^{2}

n = 1 \sum \infty 8^{n} x^{n} n!

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{- 1})

x \cdot \frac{d y}{d x} = x tan (\frac{y}{x}) + y