What is the integral of-2arctan(6x) ?

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

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integral of-2arctan(6x)

\int - 2 arctan (6 x) d x

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

Solution steps

\int - 2 arctan (6 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int arctan (6 x) d x

Apply Integration By Parts

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

= - 2 (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

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

Add a constant to the solution

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

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