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

解答

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

- arcsin (x) 1 - x^{2} + x + C

求解步骤

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

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

= \int x arcsin (x) \frac{1}{1 - x ^{2}} d x

使用分布积分法

= - arcsin (x) 1 - x^{2} - \int - 1 d x

\int - 1 d x = - x

= - arcsin (x) 1 - x^{2} - (- x)

化简

= - arcsin (x) 1 - x^{2} + x

解答补常数

= - arcsin (x) 1 - x^{2} + x + C

\int x^{i} d x

\int \frac{( x + 2 )}{x + 1} d x

x \to 1 lim (\frac{x - 1}{x ^{2} + 1})

\int 6 x + 3 d x

n = 1 \sum \infty \frac{1}{e ^{n^{3}}}