Calculus Examples

$\int (x^{π} + x^{3}) d x$

Step 1

Remove parentheses.

$\int x^{π} + x^{3} d x$

Step 2

Split the single integral into multiple integrals.

$\int x^{π} d x + \int x^{3} d x$

Step 3

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

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

Step 4

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$\frac{1}{π + 1} x^{π + 1} + C + \frac{1}{4} x^{4} + C$

Step 5

Simplify.

$\frac{1}{π + 1} x^{π + 1} + \frac{1}{4} x^{4} + C$