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

The integral of (arcsin^4(x))/(sqrt(1-x^2)) is (arcsin^5(x))/5+C

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integral of (arcsin^4(x))/(sqrt(1-x^2))

\int \frac{arcsin ^{4} ( x )}{1 - x ^{2}} d x

\frac{arcsin ^{5} ( x )}{5} + C

Solution steps

\int \frac{arcsin ^{4} ( x )}{1 - x ^{2}} d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = arcsin (x)

= \frac{arcsin ^{5} ( x )}{5}

Add a constant to the solution

= \frac{arcsin ^{5} ( x )}{5} + C

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What is the integral of (arcsin^4(x))/(sqrt(1-x^2)) ?
The integral of (arcsin^4(x))/(sqrt(1-x^2)) is (arcsin^5(x))/5+C