What is the integral of arctan(3x) ?

The integral of arctan(3x) is xarctan(3x)-1/6 ln|9x^2+1|+C

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integral of arctan(3x)

\int arctan (3 x) d x

x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1 + C

Solution steps

\int arctan (3 x) d x

Apply Integration By Parts

: x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x

= x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x

\int \frac{3 x}{9 x ^{2} + 1} d x = \frac{1}{6} ln 9 x^{2} + 1

= x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1

Add a constant to the solution

= x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1 + C

f (x) = 24 e^{x}, at x = 2

\frac{d}{d x} (ln (5 x^{2} + 1))

sin (x), \frac{1}{6} π

\frac{\partial}{\partial y} (tan (3 x - 5 y))

2^{40}

What is the integral of arctan(3x) ?
The integral of arctan(3x) is xarctan(3x)-1/6 ln|9x^2+1|+C