Calculus Examples

$f (x) = 3 + \cos (x)$

Step 1

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 2

Set up the integral to solve.

$F (x) = \int 3 + \cos (x) d x$

Step 3

Split the single integral into multiple integrals.

$\int 3 d x + \int \cos (x) d x$

Step 4

Apply the constant rule.

$3 x + C + \int \cos (x) d x$

Step 5

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

$3 x + C + \sin (x) + C$

Step 6

Simplify.

$3 x + \sin (x) + C$

Step 7

The answer is the antiderivative of the function $f (x) = 3 + \cos (x)$ .

$F (x) =$ $3 x + \sin (x) + C$