What is the integral of arctan(9x) ?

The integral of arctan(9x) is xarctan(9x)-1/18 ln|81x^2+1|+C

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integral of arctan(9x)

\int arctan (9 x) d x

x arctan (9 x) - \frac{1}{18} ln 81 x^{2} + 1 + C

Solution steps

\int arctan (9 x) d x

Apply Integration By Parts

: x arctan (9 x) - \int \frac{9 x}{81 x ^{2} + 1} d x

= x arctan (9 x) - \int \frac{9 x}{81 x ^{2} + 1} d x

\int \frac{9 x}{81 x ^{2} + 1} d x = \frac{1}{18} ln 81 x^{2} + 1

= x arctan (9 x) - \frac{1}{18} ln 81 x^{2} + 1

Add a constant to the solution

= x arctan (9 x) - \frac{1}{18} ln 81 x^{2} + 1 + C

f (x) = \frac{1}{x} + \frac{1}{x ^{2}}

\frac{( 5 x ^{5} - 3 x ^{2} + 1 )}{x}

\int \frac{1}{12 ( x ^{2} + 1 )} d x

x \to 3 + lim (\frac{x}{x - 3})

(1 + x) y^{^{'}} - x y = x + x^{2}

What is the integral of arctan(9x) ?
The integral of arctan(9x) is xarctan(9x)-1/18 ln|81x^2+1|+C