## Answer

## Step by step solution

Problem

The integral of a sum of two or more functions is equal to the sum of their integrals

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

Solve the integral $\int e^{5x}dx$ applying u-substitution. Let $u$ and $du$ be

Isolate $dx$ in the previous equation

Substituting $u$ and $dx$ in the integral

Taking the constant out of the integral

The integral of the exponential function is given by the following formula $\displaystyle \int a^xdx=\frac{a^x}{\ln(a)}$, where $a > 0$ and $a \neq 1$

Substitute $u$ back for it's value, $5x$

Add the constant of integration