Calculus Examples

$\int 5 e^{5} x d x$

Step 1

Since $5 e^{5}$ is constant with respect to $x$ , move $5 e^{5}$ out of the integral.

$5 e^{5} \int x d x$

Step 2

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$5 e^{5} (\frac{1}{2} x^{2} + C)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite $5 e^{5} (\frac{1}{2} x^{2} + C)$ as $5 e^{5} \frac{1}{2} x^{2} + C$ .

$5 e^{5} \frac{1}{2} x^{2} + C$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Combine $\frac{1}{2}$ and $5$ .

$\frac{5}{2} e^{5} x^{2} + C$

Step 3.2.2

Combine $\frac{5}{2}$ and $e^{5}$ .

$\frac{5 e^{5}}{2} x^{2} + C$