# Math Help - integration problem

1. ## integration problem

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?

2. Originally Posted by clockingly
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?
That's correct, but why didn't you check it by differentiating your answer