What is the integral of arctan(2x) ?

The integral of arctan(2x) is xarctan(2x)-1/4 ln|4x^2+1|+C

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integral of arctan(2x)

\int arctan (2 x) d x

x arctan (2 x) - \frac{1}{4} ln 4 x^{2} + 1 + C

Solution steps

\int arctan (2 x) d x

Apply Integration By Parts

: x arctan (2 x) - \int \frac{2 x}{4 x ^{2} + 1} d x

= x arctan (2 x) - \int \frac{2 x}{4 x ^{2} + 1} d x

\int \frac{2 x}{4 x ^{2} + 1} d x = \frac{1}{4} ln 4 x^{2} + 1

= x arctan (2 x) - \frac{1}{4} ln 4 x^{2} + 1

Add a constant to the solution

= x arctan (2 x) - \frac{1}{4} ln 4 x^{2} + 1 + C

\frac{\partial}{\partial x} (10 (11 x - 3 y + 12)^{5})

\frac{d}{d x} (x - \frac{3}{2})

\int csc^{2} (y) \frac{1}{1 + cot ( y )} d y

\frac{d}{d x} (\frac{x ^{2}}{y ^{3}})

What is the integral of arctan(2x) ?
The integral of arctan(2x) is xarctan(2x)-1/4 ln|4x^2+1|+C