integral of 1/(sqrt(2-5x^2))

解答

\int \frac{1}{2 - 5 x ^{2}} d x

\frac{1}{5} arcsin (\frac{5}{2} x) + C

求解步骤

\int \frac{1}{2 - 5 x ^{2}} d x

使用三角换元法

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

提出常数:

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

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

常数积分:

\int a d x = a x

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

u = arcsin (\frac{5}{2} x)

代回

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

化简

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

= \frac{1}{5} arcsin (\frac{5}{2} x)

解答补常数

= \frac{1}{5} arcsin (\frac{5}{2} x) + C

\frac{d}{d x} (\frac{( sin ( x ) )}{1 + cos ( x )})

x \to 0 + lim (x ln (3 x))

d er i v a t i v e \frac{6 x}{5 - cot ( x )}

d er i v a t i v e e^{2 x^{2 x}}

x \to 1 lim ((x - 1)^{- 1})