Calculus Examples

$\frac{2}{x^{2} + 1}$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

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

Step 2

Simplify the expression.

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Step 2.1

Reorder $x^{2}$ and $1$ .

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

Step 2.2

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

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

Step 3

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

$2 (\arctan (x) + C)$

Step 4

Simplify.

$2 \arctan (x) + C$