What is the integral of x^5arctan(x^2) ?

The integral of x^5arctan(x^2) is 1/6 x^6arctan(x^2)-1/12 (x^4+1-ln|x^4+1|)+C

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integral of x^5arctan(x^2)

\int x^{5} arctan (x^{2}) d x

\frac{1}{6} x^{6} arctan (x^{2}) - \frac{1}{12} (x^{4} + 1 - ln x^{4} + 1) + C

Solution steps

\int x^{5} arctan (x^{2}) d x

Apply Integration By Parts

: \frac{1}{6} x^{6} arctan (x^{2}) - \int \frac{x ^{7}}{3 ( x ^{4} + 1 )} d x

= \frac{1}{6} x^{6} arctan (x^{2}) - \int \frac{x ^{7}}{3 ( x ^{4} + 1 )} d x

\int \frac{x ^{7}}{3 ( x ^{4} + 1 )} d x = \frac{1}{12} (x^{4} + 1 - ln x^{4} + 1)

= \frac{1}{6} x^{6} arctan (x^{2}) - \frac{1}{12} (x^{4} + 1 - ln x^{4} + 1)

Add a constant to the solution

= \frac{1}{6} x^{6} arctan (x^{2}) - \frac{1}{12} (x^{4} + 1 - ln x^{4} + 1) + C

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What is the integral of x^5arctan(x^2) ?
The integral of x^5arctan(x^2) is 1/6 x^6arctan(x^2)-1/12 (x^4+1-ln|x^4+1|)+C