What is the integral of+arctan(7x) ?

The integral of+arctan(7x) is xarctan(7x)-1/14 ln|49x^2+1|+C

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integral of+arctan(7x)

\int + arctan (7 x) d x

x arctan (7 x) - \frac{1}{14} ln 49 x^{2} + 1 + C

Solution steps

\int arctan (7 x) d x

Apply Integration By Parts

: x arctan (7 x) - \int \frac{7 x}{49 x ^{2} + 1} d x

= x arctan (7 x) - \int \frac{7 x}{49 x ^{2} + 1} d x

\int \frac{7 x}{49 x ^{2} + 1} d x = \frac{1}{14} ln 49 x^{2} + 1

= x arctan (7 x) - \frac{1}{14} ln 49 x^{2} + 1

Add a constant to the solution

= x arctan (7 x) - \frac{1}{14} ln 49 x^{2} + 1 + C

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What is the integral of+arctan(7x) ?
The integral of+arctan(7x) is xarctan(7x)-1/14 ln|49x^2+1|+C