Calculus Examples

$\int \frac{15}{25 + x^{2}} d x d x$

Step 1

Since $15$ is constant with respect to $x$ , move $15$ out of the integral.

$15 \int \frac{1}{25 + x^{2}} d x d x$

Step 2

Rewrite $25$ as $5^{2}$ .

$15 \int \frac{1}{5^{2} + x^{2}} d x d x$

Step 3

The integral of $\frac{1}{5^{2} + x^{2}}$ with respect to $x$ is $\frac{1}{5} \arctan (\frac{x}{5}) + C$ .

$15 (\frac{1}{5} \arctan (\frac{x}{5}) + C) d x$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Combine $\frac{1}{5}$ and $\arctan (\frac{x}{5})$ .

$15 (\frac{\arctan (\frac{x}{5})}{5} + C) d x$

Step 4.2

Rewrite $15 (\frac{\arctan (\frac{x}{5})}{5} + C) d x$ as $3 \arctan (\frac{x}{5}) d x + C$ .

$3 \arctan (\frac{x}{5}) d x + C$

Step 4.3

Reorder terms.

$3 \arctan (\frac{1}{5} x) d x + C$