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

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

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integral of (u^2)/((u^2+1))

integral

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

- arctan (u) + u + C

Solution steps

\int \frac{u ^{2}}{u ^{2} + 1} d u

\frac{u ^{2}}{u ^{2} + 1} = - \frac{1}{u ^{2} + 1} + 1

= \int - \frac{1}{u ^{2} + 1} + 1 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{u ^{2} + 1} d u + \int 1 d u

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

\int 1 d u = u

= - arctan (u) + u

Add a constant to the solution

= - arctan (u) + u + C

cos^{4} (x) sin^{5} (x)

3^{x + 2}

\frac{1}{( a ^{2} + x ^{2} ) ^{0.5}}

\frac{sin ^{2} ( x )}{( 1 + sin ( x ) )}

\frac{3}{x ( x + 3 )}

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