Calculus Examples

$\int \frac{3}{16 + x^{2}} d x$

Step 1

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \frac{1}{16 + x^{2}} d x$

Step 2

Rewrite $16$ as $4^{2}$ .

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

Step 3

The integral of $\frac{1}{4^{2} + x^{2}}$ with respect to $x$ is $\frac{1}{4} \arctan (\frac{x}{4}) + C$ .

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

Step 4

Simplify the answer.

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Step 4.1

Combine $\frac{1}{4}$ and $\arctan (\frac{x}{4})$ .

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

Step 4.2

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

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

Step 4.3

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

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