How do you evaluate the integral inte^(4x) dx?

1 Answer
Aug 13, 2014

We will use u-substitution, letting u = 4x.

Thus, du = 4dx.

Also, we will use the constant law of integration, namely int C*f(x)dx = C*int f(x) dx to rewrite the integral so that it contains du:

int e^(4x)dx = 1/4 int 4*e^(4x)dx

Now, we will rewrite in terms of u:

int e^(4x)dx = 1/4 int e^(u)du

We know that the integral of e^u du will simply be e^u. Remember the constant of integration:

int e^(4x)dx = 1/4 e^(u) + C

Substituting back u gives:

int e^(4x)dx = 1/4 e^(4x) + C