Calculus Examples

$\int \frac{4}{x^{2} + 9} d x$

Step 1

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int \frac{1}{x^{2} + 9} d x$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Reorder $x^{2}$ and $9$ .

$4 \int \frac{1}{9 + x^{2}} d x$

Step 2.2

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

$4 \int \frac{1}{3^{2} + x^{2}} d x$

Step 3

The integral of $\frac{1}{3^{2} + x^{2}}$ with respect to $x$ is $\frac{1}{3} \arctan (\frac{x}{3}) + C$ .

$4 (\frac{1}{3} \arctan (\frac{x}{3}) + C)$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Combine $\frac{1}{3}$ and $\arctan (\frac{x}{3})$ .

$4 (\frac{\arctan (\frac{x}{3})}{3} + C)$

Step 4.2

Rewrite $4 (\frac{\arctan (\frac{x}{3})}{3} + C)$ as $4 (\frac{1}{3}) \arctan (\frac{1}{3} x) + C$ .

$4 (\frac{1}{3}) \arctan (\frac{1}{3} x) + C$

Step 4.3

Combine $4$ and $\frac{1}{3}$ .

$\frac{4}{3} \arctan (\frac{1}{3} x) + C$