Calculus Examples

$\int \frac{1}{x \sqrt{x^{4} - 1}} d x$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 1.2

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

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

Step 2

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

$arcsec (| x^{2} |) + C$

Step 3

Rewrite $arcsec (| x^{2} |) + C$ as $arcsec (x^{2}) + C$ .

$arcsec (x^{2}) + C$