# Math Help - finding an integral

1. ## finding an integral

Find the integral of:

[e^[3ln(x)] + e^(3x)] dx

2. Originally Posted by DINOCALC09
Find the integral of:

[e^[3ln(x)] + e^(3x)] dx
First, let's simplify the integrand:

$e^{3ln(x)} + e^{3x} = x^3+e^{3x}$

The integral of that is:

$\frac{x^4}{4} + \frac{e^{3x}}{3}$

3. for the integral of e and its power dont u multiply it by the coefficient of x (chain rule) instead of dividing?

4. ignore what i said above- woops, my bad. you did it right

5. Say we have: $e^{ln(x^a)}$

Obviously, it equals $x^a$

Also, $e^{ln(x^a)} = e^{aln(x)}$

Let a = 3

$e^{3ln(x)} = e^{ln(x)+ln(x)+ln(x)} \Rightarrow e^{ln(x)}e^{ln(x)}e^{ln(x)} = x*x*x$