What is the integral of xarctan(6x) ?

The integral of xarctan(6x) is 1/2 x^2arctan(6x)-1/72 (-arctan(6x)+6x)+C

Popular >

integral of xarctan(6x)

\int x arctan (6 x) d x

\frac{1}{2} x^{2} arctan (6 x) - \frac{1}{72} (- arctan (6 x) + 6 x) + C

Solution steps

\int x arctan (6 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} arctan (6 x) - \int \frac{3 x ^{2}}{36 x ^{2} + 1} d x

= \frac{1}{2} x^{2} arctan (6 x) - \int \frac{3 x ^{2}}{36 x ^{2} + 1} d x

\int \frac{3 x ^{2}}{36 x ^{2} + 1} d x = \frac{1}{72} (- arctan (6 x) + 6 x)

= \frac{1}{2} x^{2} arctan (6 x) - \frac{1}{72} (- arctan (6 x) + 6 x)

Add a constant to the solution

= \frac{1}{2} x^{2} arctan (6 x) - \frac{1}{72} (- arctan (6 x) + 6 x) + C

\frac{\partial}{\partial y} (x^{2} yz)

\frac{\partial}{\partial r} (r cos (t))

n = 1 \sum \infty \frac{n ^{6}}{6 ^{n}}

\int \frac{w}{w ^{3} + w ^{2} + 4 w + 4} d w

\int e^{- 3 x} sin (x) d x

What is the integral of xarctan(6x) ?
The integral of xarctan(6x) is 1/2 x^2arctan(6x)-1/72 (-arctan(6x)+6x)+C