Calculus Examples

$\int 2 + x^{3} + x^{6} d x$

Step 1

Split the single integral into multiple integrals.

$\int 2 d x + \int x^{3} d x + \int x^{6} d x$

Step 2

Apply the constant rule.

$2 x + C + \int x^{3} d x + \int x^{6} d x$

Step 3

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

$2 x + C + \frac{1}{4} x^{4} + C + \int x^{6} d x$

Step 4

By the Power Rule, the integral of $x^{6}$ with respect to $x$ is $\frac{1}{7} x^{7}$ .

$2 x + C + \frac{1}{4} x^{4} + C + \frac{1}{7} x^{7} + C$

Step 5

Simplify.

$2 x + \frac{1}{4} x^{4} + \frac{1}{7} x^{7} + C$