Calculus Examples

$\int (2 + \tan^{2} (θ)) d θ$

Step 1

Remove parentheses.

$\int 2 + \tan^{2} (θ) d θ$

Step 2

Split the single integral into multiple integrals.

$\int 2 d θ + \int \tan^{2} (θ) d θ$

Step 3

Apply the constant rule.

$2 θ + C + \int \tan^{2} (θ) d θ$

Step 4

Using the Pythagorean Identity, rewrite $\tan^{2} (θ)$ as $- 1 + \sec^{2} (θ)$ .

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

Step 5

Split the single integral into multiple integrals.

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

Step 6

Apply the constant rule.

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

Step 7

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

$2 θ + C - θ + C + \tan (θ) + C$

Step 8

Simplify.

Tap for more steps...

Step 8.1

Subtract $θ$ from $2 θ$ .

$C + θ + C + \tan (θ) + C$

Step 8.2

Simplify.

$θ + \tan (θ) + C$