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

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

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integral of x^2arctan(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (x^{3} - 4 x)

\frac{d ^{3}}{d x ^{3}} (\frac{7}{x ^{2}})

\frac{\partial}{\partial x} (a^{x})

\int \frac{5 x}{( x ^{2} + 5 ) ^{2}} d x

\frac{d}{d x} (- cos (\frac{x}{2}))

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