Calculus Examples

$\int (\sec^{2} (x) - 1) d x$

Step 1

Remove parentheses.

$\int \sec^{2} (x) - 1 d x$

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

$\tan (x) + C + \int - 1 d x$

Step 4

Apply the constant rule.

$\tan (x) + C - x + C$

Step 5

Simplify.

$\tan (x) - x + C$