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

The integral of x^2arctan(3x) is 1/3 x^3arctan(3x)-1/162 (9x^2+1-ln|9x^2+1|)+C

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integral of x^2arctan(3x)

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

\frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1) + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} arctan (3 x) - \int \frac{x ^{3}}{9 x ^{2} + 1} d x

= \frac{1}{3} x^{3} arctan (3 x) - \int \frac{x ^{3}}{9 x ^{2} + 1} d x

\int \frac{x ^{3}}{9 x ^{2} + 1} d x = \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1)

Add a constant to the solution

= \frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1) + C

\frac{\partial}{\partial x} (4 x + 5)

f (x) = x^{2} - 3

x^{2} y^{^{'}} = y - x y

\frac{d}{d x} (2 (sin (x^{2}) + 2 x^{2} cos (x^{2})))

What is the integral of x^2arctan(3x) ?
The integral of x^2arctan(3x) is 1/3 x^3arctan(3x)-1/162 (9x^2+1-ln|9x^2+1|)+C