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)

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

- 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

k = 1 \sum \infty \frac{k}{2 ^{k}}

\frac{d}{d x} (cosh (x^{2}))

\frac{\partial}{\partial p} (p^{3} q^{2} + 2 pq + \frac{p}{q})

\int \frac{3 x ^{2}}{x ^{3} - 1} d x

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