Calculus Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

$\arctan (x) + C$