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

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

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integral of (x*arcsin(x))/(sqrt(1-x^2))

\int \frac{x \cdot 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

\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

d er i v a t i v e - x e^{- x} + e^{- x}

\frac{d}{d x} (2 e^{x} + e^{x} x)

y^{^{'}} = 20 x y

\frac{d}{d x} (\frac{x}{x - 6})

\int \frac{1}{4} x^{2} d x

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