Calculus Examples

$\int \frac{4 e^{2}}{x^{- 3}} d x$

Step 1

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\int 4 e^{2} x^{3} d x$

Step 2

Since $4 e^{2}$ is constant with respect to $x$ , move $4 e^{2}$ out of the integral.

$4 e^{2} \int x^{3} d x$

Step 3

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

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

Step 4

Simplify the answer.

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Step 4.1

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

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

Step 4.2

Simplify.

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Step 4.2.1

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

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

Step 4.2.2

Combine $\frac{4}{4}$ and $e^{2}$ .

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

Step 4.2.3

Cancel the common factor of $4$ .

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Step 4.2.3.1

Cancel the common factor.

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

Step 4.2.3.2

Divide $e^{2}$ by $1$ .

$e^{2} x^{4} + C$