Calculus Examples

$\int 6 + u + u^{2} d u$

Step 1

Split the single integral into multiple integrals.

$\int 6 d u + \int u d u + \int u^{2} d u$

Step 2

Apply the constant rule.

$6 u + C + \int u d u + \int u^{2} d u$

Step 3

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

$6 u + C + \frac{1}{2} u^{2} + C + \int u^{2} d u$

Step 4

By the Power Rule, the integral of $u^{2}$ with respect to $u$ is $\frac{1}{3} u^{3}$ .

$6 u + C + \frac{1}{2} u^{2} + C + \frac{1}{3} u^{3} + C$

Step 5

Simplify.

$6 u + \frac{1}{2} u^{2} + \frac{1}{3} u^{3} + C$