Calculus Examples

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

Step 1

Simplify.

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Step 1.1

Use logarithm rules to move $x$ out of the exponent.

$\int x \ln (e) d x$

Step 1.2

The natural logarithm of $e$ is $1$ .

$\int x \cdot 1 d x$

Step 1.3

Multiply $x$ by $1$ .

$\int x d x$

Step 2

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

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