What is the integral of xarctan(18x) ?

The integral of xarctan(18x) is 1/2 x^2arctan(18x)-1/648 (-arctan(18x)+18x)+C

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integral of xarctan(18x)

\int x arctan (18 x) d x

\frac{1}{2} x^{2} arctan (18 x) - \frac{1}{648} (- arctan (18 x) + 18 x) + C

Solution steps

\int x arctan (18 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} arctan (18 x) - \int \frac{9 x ^{2}}{324 x ^{2} + 1} d x

= \frac{1}{2} x^{2} arctan (18 x) - \int \frac{9 x ^{2}}{324 x ^{2} + 1} d x

\int \frac{9 x ^{2}}{324 x ^{2} + 1} d x = \frac{1}{648} (- arctan (18 x) + 18 x)

= \frac{1}{2} x^{2} arctan (18 x) - \frac{1}{648} (- arctan (18 x) + 18 x)

Add a constant to the solution

= \frac{1}{2} x^{2} arctan (18 x) - \frac{1}{648} (- arctan (18 x) + 18 x) + C

\int t sec^{2} (6 t) d t

n = 0 \sum \infty \frac{1}{1. 1 ^{n}}

\frac{d}{d x} (x^{4} + 8 x^{3} + 6 x^{2} - 40 x + 25)

x y^{^{'}} + 2 y = - 3 sin (x)

\int \frac{x ^{3}}{64 - x ^{2}} d x

What is the integral of xarctan(18x) ?
The integral of xarctan(18x) is 1/2 x^2arctan(18x)-1/648 (-arctan(18x)+18x)+C