Calculus Examples

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

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

Step 1

Simplify the expression.

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Step 1.1

Reorder

x^{2}

$x^{2}$ and

1

$1$ .

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

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

Step 1.2

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

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

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

Step 2

The integral of

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

$\frac{1}{1^{2} + x^{2}}$ with respect to

x

$x$ is

\arctan (x) + C

$\arctan (x) + C$ .

\arctan (x) + C

$\arctan (x) + C$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$