Calculus Examples

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

Step 1

This integral could not be completed using u-substitution. Mathway will use another method.

Step 2

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

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

Step 3

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

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

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

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

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

Step 4.2

Simplify.

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

Step 4.3

Simplify.

Tap for more steps...

Step 4.3.1

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

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

Step 4.3.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 4.3.2.1

Cancel the common factor.

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

Step 4.3.2.2

Divide $\arctan (\frac{y}{x})$ by $1$ .

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