Hi, I just did out this problem and I was wondering if someone could tell me if I did it correctly.
I had to take the integral of the cube root of 5x.
This is what I did:
The integral of the cube root of 5x is the same as (5x)^(1/3).
Therefore, I set u = 5x
This made dx = 1/5 du
Then I got the integral of u^(1/3) * 1/5
Since 1/5 is a constant, this led to:
1/5 * the integral of u^(1/3).
The integral of u^(1/3) is 3/4 u^(4/3).
Therefore, when you multiply this by 1/5, you get 3u^(4/3) divided by 20.
Replacing u with 5x, I got 3(5x)^(4/3) divided by 20 + C for a final answer.
Does this look right?