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Math Help - Help with two substitution problems

  1. #1
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    Help with two substitution problems

    The definite integral from 1 to 10 of x/x^2

    and the indefinite integral of x+2/the square root of x^2+4x


    For the first one I THINK u would be x^2 and thus du would be 2x and I'd have to divide it by two so then I'm left with 1/2 the integral of...what? Would it just be 1/u?

    And for the second again I think I know to use x^2+4x as u making du 2x+4 so I'd have 1/2 the integral of 1/the square root of u?

    If I'm correct so far just let me know and I'll keep working, preferably don't give me any other hints, but if I am wrong so far please do tell me where I'm going wrong!
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  2. #2
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    Your work is correct but there're other faster ways, but since you told us you don't need additional hints, then I'll stay away.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    Your work is correct but there're other faster ways, but since you told us you don't need additional hints, then I'll stay away.
    Well if there's a faster and better way I can go about it please do let me know! Do you mean faster than substitution, or faster as in using the same process but by a different means?
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  4. #4
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    Are you not aware that x/x^2= 1/x as long as x is not 0?
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    Are you not aware that x/x^2= 1/x as long as x is not 0?
    No I am aware...and your point is...?
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  6. #6
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    HallsofIvy's point aims that \frac x{x^2}=\frac1x provided that 1\le x\le10, hence no substitution required.
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