Calculus Examples

$\int x^{2} + y^{2} d x$

Step 1

Split the single integral into multiple integrals.

$\int x^{2} d x + \int y^{2} d x$

Step 2

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

$\frac{1}{3} x^{3} + C + \int y^{2} d x$

Step 3

Apply the constant rule.

$\frac{1}{3} x^{3} + C + y^{2} x + C$

Step 4

Simplify.

$\frac{1}{3} x^{3} + y^{2} x + C$