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

Popular >

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

= - 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

f (x) = sin^{2} (x) cos (x)

- x e^{- x} + e^{- x}

y = e^{- x} - e^{- x} x

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

\int 2 x x - \frac{1}{x} 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