Calculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

$\tan (x) + C + \int - \csc^{2} (x) d x$

Step 4

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

$\tan (x) + C - \int \csc^{2} (x) d x$

Step 5

Since the derivative of $- \cot (x)$ is $\csc^{2} (x)$ , the integral of $\csc^{2} (x)$ is $- \cot (x)$ .

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

Step 6

Simplify.

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