Calculus Examples

$\frac{\sin (x)}{\cos (x)}$

Step 1

Write $\frac{\sin (x)}{\cos (x)}$ as a function.

$f (x) = \frac{\sin (x)}{\cos (x)}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int \frac{\sin (x)}{\cos (x)} d x$

Step 4

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\int \tan (x) d x$

Step 5

The integral of $\tan (x)$ with respect to $x$ is $\ln (| \sec (x) |)$ .

$\ln (| \sec (x) |) + C$

Step 6

The answer is the antiderivative of the function $f (x) = \frac{\sin (x)}{\cos (x)}$ .

$F (x) =$ $\ln (| \sec (x) |) + C$