Calculus Examples

$\int e^{3 \ln (x)} d x$

Step 1

Simplify.

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Step 1.1

Simplify $3 \ln (x)$ by moving $3$ inside the logarithm.

$\int e^{\ln (x^{3})} d x$

Step 1.2

Exponentiation and log are inverse functions.

$\int x^{3} d x$

Step 2

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$\frac{1}{4} x^{4} + C$