Calculus Examples

$\int (θ^{6} + \sec^{2} (θ)) d θ$

Step 1

Remove parentheses.

$\int θ^{6} + \sec^{2} (θ) d θ$

Step 2

Split the single integral into multiple integrals.

$\int θ^{6} d θ + \int \sec^{2} (θ) d θ$

Step 3

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

$\frac{1}{7} θ^{7} + C + \int \sec^{2} (θ) d θ$

Step 4

Since the derivative of $\tan (θ)$ is $\sec^{2} (θ)$ , the integral of $\sec^{2} (θ)$ is $\tan (θ)$ .

$\frac{1}{7} θ^{7} + C + \tan (θ) + C$

Step 5

Simplify.

$\frac{1}{7} θ^{7} + \tan (θ) + C$