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

3 e^{t}

y^{^{''}} + 2 y^{^{'}} + y = e^{- t}, y (0) = - 1, y^{^{'}} (0) = 1

\frac{d}{d x} (\frac{60}{x ^{4}})

x \to 2 lim (\frac{x ^{2} - 1}{x - 1})

n = 0 \sum \infty arctan (n)

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