What is the integral of arctan(8x) ?

The integral of arctan(8x) is xarctan(8x)-1/16 ln|64x^2+1|+C

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integral of arctan(8x)

\int arctan (8 x) d x

x arctan (8 x) - \frac{1}{16} ln 64 x^{2} + 1 + C

Solution steps

\int arctan (8 x) d x

Apply Integration By Parts

: x arctan (8 x) - \int \frac{8 x}{64 x ^{2} + 1} d x

= x arctan (8 x) - \int \frac{8 x}{64 x ^{2} + 1} d x

\int \frac{8 x}{64 x ^{2} + 1} d x = \frac{1}{16} ln 64 x^{2} + 1

= x arctan (8 x) - \frac{1}{16} ln 64 x^{2} + 1

Add a constant to the solution

= x arctan (8 x) - \frac{1}{16} ln 64 x^{2} + 1 + C

f (x) = x (x^{3} - 8)

\frac{d y}{d x} = (1 - x) y^{2}

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

\frac{s}{( s ^{2} + 1 )}

y^{^{'}} = y cos (2 x), y (0) = 1.6

What is the integral of arctan(8x) ?
The integral of arctan(8x) is xarctan(8x)-1/16 ln|64x^2+1|+C