Calculus Examples

$\int 11 x^{2} e (- 4 x^{3}) d x$

Step 1

Simplify.

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Step 1.1

Multiply $- 4$ by $11$ .

$\int - 44 x^{2} e x^{3} d x$

Step 1.2

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

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Step 1.2.1

Move $x^{3}$ .

$\int - 44 (x^{3} x^{2}) e d x$

Step 1.2.2

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

$\int - 44 x^{3 + 2} e d x$

Step 1.2.3

Add $3$ and $2$ .

$\int - 44 x^{5} e d x$

Step 2

Since $- 44 e$ is constant with respect to $x$ , move $- 44 e$ out of the integral.

$- 44 e \int x^{5} d x$

Step 3

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

$- 44 e (\frac{1}{6} x^{6} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $- 44 e (\frac{1}{6} x^{6} + C)$ as $- 44 e \frac{1}{6} x^{6} + C$ .

$- 44 e \frac{1}{6} x^{6} + C$

Step 4.2

Simplify.

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Step 4.2.1

Combine $\frac{1}{6}$ and $- 44$ .

$\frac{- 44}{6} e x^{6} + C$

Step 4.2.2

Combine $\frac{- 44}{6}$ and $e$ .

$\frac{- 44 e}{6} x^{6} + C$

Step 4.2.3

Cancel the common factor of $- 44$ and $6$ .

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Step 4.2.3.1

Factor $2$ out of $- 44 e$ .

$\frac{2 (- 22 e)}{6} x^{6} + C$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $2$ out of $6$ .

$\frac{2 (- 22 e)}{2 (3)} x^{6} + C$

Step 4.2.3.2.2

Cancel the common factor.

$\frac{2 (- 22 e)}{2 \cdot 3} x^{6} + C$

Step 4.2.3.2.3

Rewrite the expression.

$\frac{- 22 e}{3} x^{6} + C$

Step 4.2.4

Move the negative in front of the fraction.

$- \frac{22 e}{3} x^{6} + C$