What is the integral of arctan(6x) ?

The integral of arctan(6x) is xarctan(6x)-1/12 ln|36x^2+1|+C

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integral of arctan(6x)

\int arctan (6 x) d x

x arctan (6 x) - \frac{1}{12} ln 36 x^{2} + 1 + C

Solution steps

\int arctan (6 x) d x

Apply Integration By Parts

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

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

\int \frac{6 x}{36 x ^{2} + 1} d x = \frac{1}{12} ln 36 x^{2} + 1

= x arctan (6 x) - \frac{1}{12} ln 36 x^{2} + 1

Add a constant to the solution

= x arctan (6 x) - \frac{1}{12} ln 36 x^{2} + 1 + C

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What is the integral of arctan(6x) ?
The integral of arctan(6x) is xarctan(6x)-1/12 ln|36x^2+1|+C