Calculus Examples

$\int \frac{1}{x \sqrt{25 x^{2} - 1}} d x$

Step 1

Simplify with factoring out.

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Step 1.1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$\int \frac{1}{x \sqrt{{(5 x)}^{2} - 1}} d x$

Step 1.2

Rewrite $1$ as $1^{2}$ .

$\int \frac{1}{x \sqrt{{(5 x)}^{2} - 1^{2}}} d x$

Step 2

The integral of $\frac{1}{x \sqrt{{(5 x)}^{2} - 1^{2}}}$ with respect to $x$ is $arcsec (| 5 x |)$

$arcsec (| 5 x |) + C$

Step 3

Rewrite $arcsec (| 5 x |) + C$ as $arcsec (5 | x |) + C$ .

$arcsec (5 | x |) + C$