Calculus Examples

$\int (\sin (u) + u) d u$

Step 1

Remove parentheses.

$\int \sin (u) + u d u$

Step 2

Split the single integral into multiple integrals.

$\int \sin (u) d u + \int u d u$

Step 3

The integral of $\sin (u)$ with respect to $u$ is $- \cos (u)$ .

$- \cos (u) + C + \int u d u$

Step 4

By the Power Rule, the integral of $u$ with respect to $u$ is $\frac{1}{2} u^{2}$ .

$- \cos (u) + C + \frac{1}{2} u^{2} + C$

Step 5

Simplify.

$- \cos (u) + \frac{1}{2} u^{2} + C$