Calculus Examples

$\int x^{2} e x^{3} d x$

Step 1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.1

Move $x^{3}$ .

$\int x^{3} x^{2} e d x$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int x^{3 + 2} e d x$

Step 1.3

Add $3$ and $2$ .

$\int x^{5} e d x$

Step 2

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

$e \int x^{5} d x$

Step 3

By the Power Rule, the integral of $x^{5}$ with respect to $x$ is $\frac{1}{6} x^{6}$ .

$e (\frac{1}{6} x^{6} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $e (\frac{1}{6} x^{6} + C)$ as $e \frac{1}{6} x^{6} + C$ .

$e \frac{1}{6} x^{6} + C$

Step 4.2

Combine $e$ and $\frac{1}{6}$ .

$\frac{e}{6} x^{6} + C$