integral of 6/(sqrt(25-x^2))

解答

\int \frac{6}{25 - x ^{2}} d x

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

求解步骤

\int \frac{6}{25 - x ^{2}} d x

提出常数:

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

= 6 \cdot \int \frac{1}{25 - x ^{2}} d x

使用三角换元法

= 6 \cdot \int 1 d u

常数积分:

\int a d x = a x

= 6 \cdot 1 \cdot u

u = arcsin (\frac{1}{5} x)

代回

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

化简

= 6 arcsin (\frac{1}{5} x)

解答补常数

= 6 arcsin (\frac{1}{5} x) + C

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = 3 t^{2} - t^{3}

f (t) = 6 t - 6 e^{t}

\int_{2}^{\infty} e^{- 7 p} d p

x \to - 2 lim (\frac{4}{x + 2})

\frac{d}{d x} (\frac{6 x}{x ^{2} + 4})