Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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