Calculus Examples

$e^{\ln (x)}$

Step 1

Write $e^{\ln (x)}$ as a function.

$f (x) = e^{\ln (x)}$

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.

$F (x) = \int e^{\ln (x)} d x$

Step 4

Exponentiation and log are inverse functions.

$\int x d x$

Step 5

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

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

Step 6

The answer is the antiderivative of the function $f (x) = e^{\ln (x)}$ .

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