Calculus Examples

$\int (\sec^{2} (θ) - \sin (θ)) d θ$

Step 1

Remove parentheses.

$\int \sec^{2} (θ) - \sin (θ) d θ$

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

$\tan (θ) + C + \int - \sin (θ) d θ$

Step 4

Since $- 1$ is constant with respect to $θ$ , move $- 1$ out of the integral.

$\tan (θ) + C - \int \sin (θ) d θ$

Step 5

The integral of $\sin (θ)$ with respect to $θ$ is $- \cos (θ)$ .

$\tan (θ) + C - (- \cos (θ) + C)$

Step 6

Simplify.

$\tan (θ) + \cos (θ) + C$