Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

$\frac{\arctan (\frac{x}{y})}{y} + C$