What is the integral of x^2arcsin(x^3) ?

The integral of x^2arcsin(x^3) is 1/3 x^3arcsin(x^3)+1/3 sqrt(1-x^6)+C

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integral of x^2arcsin(x^3)

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

\frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} arcsin (x^{3}) - \int \frac{x ^{5}}{1 - x ^{6}} d x

= \frac{1}{3} x^{3} arcsin (x^{3}) - \int \frac{x ^{5}}{1 - x ^{6}} d x

\int \frac{x ^{5}}{1 - x ^{6}} d x = - \frac{1}{3} 1 - x^{6}

= \frac{1}{3} x^{3} arcsin (x^{3}) - (- \frac{1}{3} 1 - x^{6})

Simplify

= \frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6}

Add a constant to the solution

= \frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6} + C

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What is the integral of x^2arcsin(x^3) ?
The integral of x^2arcsin(x^3) is 1/3 x^3arcsin(x^3)+1/3 sqrt(1-x^6)+C