What is the integral of (arcsin^3(x))/(sqrt(1-x^2)) ?

The integral of (arcsin^3(x))/(sqrt(1-x^2)) is (arcsin^4(x))/4+C

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integral of (arcsin^3(x))/(sqrt(1-x^2))

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

\frac{arcsin ^{4} ( x )}{4} + C

Solution steps

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = arcsin (x)

= \frac{arcsin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{arcsin ^{4} ( x )}{4} + C

\int t^{2} + 1 d t

\frac{d}{d x} (x - 2 y)

f (x) = x^{2} - 2 x - 8, at x = - 2

y = \frac{( 3 x + 1 )}{2}, y = x^{2} - 2

x y \frac{d y}{d x} + y^{2} = 32 x

What is the integral of (arcsin^3(x))/(sqrt(1-x^2)) ?
The integral of (arcsin^3(x))/(sqrt(1-x^2)) is (arcsin^4(x))/4+C