Calculus Examples

$f (x) = 4 x$

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.

$F (x) = \int 4 x d x$

Step 3

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int x d x$

Step 4

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

$4 (\frac{1}{2} x^{2} + C)$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Rewrite $4 (\frac{1}{2} x^{2} + C)$ as $4 (\frac{1}{2}) x^{2} + C$ .

$4 (\frac{1}{2}) x^{2} + C$

Step 5.2

Simplify.

Tap for more steps...

Step 5.2.1

Combine $4$ and $\frac{1}{2}$ .

$\frac{4}{2} x^{2} + C$

Step 5.2.2

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 5.2.2.1

Factor $2$ out of $4$ .

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

Step 5.2.2.2

Cancel the common factors.

Tap for more steps...

Step 5.2.2.2.1

Factor $2$ out of $2$ .

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

Step 5.2.2.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 1} x^{2} + C$

Step 5.2.2.2.3

Rewrite the expression.

$\frac{2}{1} x^{2} + C$

Step 5.2.2.2.4

Divide $2$ by $1$ .

$2 x^{2} + C$

Step 6

The answer is the antiderivative of the function $f (x) = 4 x$ .

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