What is the integral of (arctan(x))/(x^2+1) ?

The integral of (arctan(x))/(x^2+1) is (arctan^2(x))/2+C

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integral of (arctan(x))/(x^2+1)

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

\frac{arctan ^{2} ( x )}{2} + C

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = arctan (x)

= \frac{arctan ^{2} ( x )}{2}

Add a constant to the solution

= \frac{arctan ^{2} ( x )}{2} + C

e^{x}, 2

\int \frac{a x + b}{c x + d} d x

\frac{d}{d x} (\frac{4 x ^{\frac{3}{2}}}{x})

\int 10 x - 3 x^{2} - x^{3} d x

x (\frac{d y}{d x}) + 2 y = 0

What is the integral of (arctan(x))/(x^2+1) ?
The integral of (arctan(x))/(x^2+1) is (arctan^2(x))/2+C