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

The integral of x^2arctan(2x) is 1/3 x^3arctan(2x)-1/48 (4x^2+1-ln|4x^2+1|)+C

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integral of x^2arctan(2x)

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

\frac{1}{3} x^{3} arctan (2 x) - \frac{1}{48} (4 x^{2} + 1 - ln 4 x^{2} + 1) + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2 x ^{3}}{3 ( 4 x ^{2} + 1 )} d x = \frac{1}{48} (4 x^{2} + 1 - ln 4 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (2 x) - \frac{1}{48} (4 x^{2} + 1 - ln 4 x^{2} + 1)

Add a constant to the solution

= \frac{1}{3} x^{3} arctan (2 x) - \frac{1}{48} (4 x^{2} + 1 - ln 4 x^{2} + 1) + C

x \to \infty lim (- 11)

\frac{\partial}{\partial x} (2 + x + y e^{y})

\int \frac{8 - 8 x}{1 - x} d x

x \to 0 lim (x + \frac{1}{x})

y = ln (x^{3}) x = 12

What is the integral of x^2arctan(2x) ?
The integral of x^2arctan(2x) is 1/3 x^3arctan(2x)-1/48 (4x^2+1-ln|4x^2+1|)+C