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

The integral of x^2arctan(x^3) is 1/3 x^3arctan(x^3)-1/6 ln|x^6+1|+C

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integral of x^2arctan(x^3)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x ^{5}}{x ^{6} + 1} d x = \frac{1}{6} ln x^{6} + 1

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

Add a constant to the solution

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

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What is the integral of x^2arctan(x^3) ?
The integral of x^2arctan(x^3) is 1/3 x^3arctan(x^3)-1/6 ln|x^6+1|+C