Calculus Examples

$\frac{1}{8} \cdot \int {(4 x^{2} + 1)}^{- 5} d u$

Step 1

Since $\frac{1}{8}$ is constant with respect to $x$ , the derivative of $\frac{1}{8} \int {(4 x^{2} + 1)}^{- 5} d u$ with respect to $x$ is $\frac{1}{8} \frac{d}{d x} [\int {(4 x^{2} + 1)}^{- 5} d u]$ .

$\frac{1}{8} \frac{d}{d x} [\int {(4 x^{2} + 1)}^{- 5} d u]$

Step 2

Simplify.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{8} \frac{d}{d x} [\int \frac{1}{{(4 x^{2} + 1)}^{5}} d u]$

Step 2.2

Combine $\frac{1}{8}$ and $\frac{d}{d x} [\int \frac{1}{{(4 x^{2} + 1)}^{5}} d u]$ .

$\frac{\frac{d}{d x} [\int \frac{1}{{(4 x^{2} + 1)}^{5}} d u]}{8}$