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Math Help - integration problem

  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by clockingly View Post
    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
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