What is the integral of x^2arctan(7x) ?

The integral of x^2arctan(7x) is 1/3 x^3arctan(7x)-1/2058 (49x^2+1-ln|49x^2+1|)+C

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integral of x^2arctan(7x)

\int x^{2} arctan (7 x) d x

\frac{1}{3} x^{3} arctan (7 x) - \frac{1}{2058} (49 x^{2} + 1 - ln 49 x^{2} + 1) + C

Solution steps

\int x^{2} arctan (7 x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} arctan (7 x) - \int \frac{7 x ^{3}}{3 ( 49 x ^{2} + 1 )} d x

= \frac{1}{3} x^{3} arctan (7 x) - \int \frac{7 x ^{3}}{3 ( 49 x ^{2} + 1 )} d x

\int \frac{7 x ^{3}}{3 ( 49 x ^{2} + 1 )} d x = \frac{1}{2058} (49 x^{2} + 1 - ln 49 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (7 x) - \frac{1}{2058} (49 x^{2} + 1 - ln 49 x^{2} + 1)

Add a constant to the solution

= \frac{1}{3} x^{3} arctan (7 x) - \frac{1}{2058} (49 x^{2} + 1 - ln 49 x^{2} + 1) + C

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What is the integral of x^2arctan(7x) ?
The integral of x^2arctan(7x) is 1/3 x^3arctan(7x)-1/2058 (49x^2+1-ln|49x^2+1|)+C