Calculus Examples

$\frac{5}{4 + x^{2}}$

Step 1

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int \frac{1}{4 + x^{2}} d x$

Step 2

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

$5 \int \frac{1}{2^{2} + x^{2}} d x$

Step 3

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

$5 (\frac{1}{2} \arctan (\frac{x}{2}) + C)$

Step 4

Simplify the answer.

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Step 4.1

Combine $\frac{1}{2}$ and $\arctan (\frac{x}{2})$ .

$5 (\frac{\arctan (\frac{x}{2})}{2} + C)$

Step 4.2

Rewrite $5 (\frac{\arctan (\frac{x}{2})}{2} + C)$ as $5 (\frac{1}{2}) \arctan (\frac{1}{2} x) + C$ .

$5 (\frac{1}{2}) \arctan (\frac{1}{2} x) + C$

Step 4.3

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} \arctan (\frac{1}{2} x) + C$