1. ## integration by substitution

I am unsure if I am doing the next to the last step correctly.

integral e^5x dx
g(u) = 1/6*u^6
u = 5x
du = 5

1/6 * 1/du * u^6
1/30 (5x)^6

2. Originally Posted by startingover
I am unsure if I am doing the next to the last step correctly.

integral e^5x dx
g(u) = 1/6*u^6
u = 5x
du = 5

1/6 * 1/du * u^6
1/30 (5x)^6
Your result is wrong. You have used the wrong formula.
Notice that e^(5x) is NOT a power function. It is an exponential function.

3. Originally Posted by startingover
I am unsure if I am doing the next to the last step correctly.

integral e^5x dx
g(u) = 1/6*u^6
u = 5x
du = 5

1/6 * 1/du * u^6
1/30 (5x)^6
Yes, curvature is right. The standard way to do this is by substitution, which seems to be what you attempted.

However, it is probably best to just remember that:

$\int e^{kx} dx = \frac {1}{k} e^{kx} + C$ for $k \neq 0$