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

The integral of x^2arctan(2x^3) is 1/3 x^3arctan(2x^3)-1/12 ln|4x^6+1|+C

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integral of x^2arctan(2x^3)

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

\frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1 + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} arctan (2 x^{3}) - \int \frac{2 x ^{5}}{4 x ^{6} + 1} d x

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \int \frac{2 x ^{5}}{4 x ^{6} + 1} d x

\int \frac{2 x ^{5}}{4 x ^{6} + 1} d x = \frac{1}{12} ln 4 x^{6} + 1

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1

Add a constant to the solution

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1 + C

\int \frac{1}{x x ^{2} + 36} d x

\int \frac{1}{u ln ( u )} d u

\int 3^{t^{2}} d t

\frac{d}{d x} (\frac{3 + 2 x}{x})

\frac{d ^{3}}{d x ^{3}} (6 t + 3)

What is the integral of x^2arctan(2x^3) ?
The integral of x^2arctan(2x^3) is 1/3 x^3arctan(2x^3)-1/12 ln|4x^6+1|+C