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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = arctan (y)

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

Add a constant to the solution

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

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