Calculus Examples

$\frac{1}{\sqrt{9 - x^{2}}}$

Step 1

Rewrite $9$ as $3^{2}$ .

$\int \frac{1}{\sqrt{3^{2} - x^{2}}} d x$

Step 2

The integral of $\frac{1}{\sqrt{3^{2} - x^{2}}}$ with respect to $x$ is $\arcsin (\frac{x}{3})$

$\arcsin (\frac{x}{3}) + C$

Step 3

Rewrite $\arcsin (\frac{x}{3}) + C$ as $\arcsin (\frac{1}{3} x) + C$ .

$\arcsin (\frac{1}{3} x) + C$