Calculus Examples

$f (x) = 5 x$

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.

$F (x) = \int 5 x d x$

Step 3

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int x d x$

Step 4

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$5 (\frac{1}{2} x^{2} + C)$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Rewrite $5 (\frac{1}{2} x^{2} + C)$ as $5 (\frac{1}{2}) x^{2} + C$ .

$5 (\frac{1}{2}) x^{2} + C$

Step 5.2

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} x^{2} + C$

Step 6

The answer is the antiderivative of the function $f (x) = 5 x$ .

$F (x) =$ $\frac{5}{2} x^{2} + C$