What is the integral of (xarcsin(x))/(sqrt(1-x^2)) ?

The integral of (xarcsin(x))/(sqrt(1-x^2)) is -arcsin(x)sqrt(1-x^2)+x+C

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

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

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

Solution steps

\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

Apply Integration By Parts

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

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

\int - 1 d x = - x

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

Simplify

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

Add a constant to the solution

= - 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}}}

What is the integral of (xarcsin(x))/(sqrt(1-x^2)) ?
The integral of (xarcsin(x))/(sqrt(1-x^2)) is -arcsin(x)sqrt(1-x^2)+x+C