Calculus Examples

$\int \frac{1}{x \sqrt{64 x^{2} - 49}} d x$

Step 1

Simplify with factoring out.

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Step 1.1

Rewrite $64 x^{2}$ as ${(8 x)}^{2}$ .

$\int \frac{1}{x \sqrt{{(8 x)}^{2} - 49}} d x$

Step 1.2

Rewrite $49$ as $7^{2}$ .

$\int \frac{1}{x \sqrt{{(8 x)}^{2} - 7^{2}}} d x$

Step 2

The integral of $\frac{1}{x \sqrt{{(8 x)}^{2} - 7^{2}}}$ with respect to $x$ is $\frac{1}{7} arcsec (| \frac{8 x}{7} |)$

$\frac{1}{7} arcsec (| \frac{8 x}{7} |) + C$

Step 3

Simplify the answer.

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Step 3.1

Combine $\frac{1}{7}$ and $arcsec (| \frac{8 x}{7} |)$ .

$\frac{arcsec (| \frac{8 x}{7} |)}{7} + C$

Step 3.2

Rewrite $\frac{arcsec (| \frac{8 x}{7} |)}{7} + C$ as $\frac{arcsec (\frac{8 | x |}{7})}{7} + C$ .

$\frac{arcsec (\frac{8 | x |}{7})}{7} + C$

Step 3.3

Reorder terms.

$\frac{1}{7} arcsec (\frac{8}{7} | x |) + C$