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Math Help - Is this an improper integral?

  1. #1
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    Is this an improper integral?

    I have to integrate Int(-1,1)(x2 ln(x+5))dx

    sorry for this way to write, but I didn't figure out the code to write it in proper form.

    This integral is improper because it's not defined for x<=-5.

    Is this true? How would you solve this integral in a fast way? I tried, but I always get stuck doing all the calculations. Can anyone give me some hint? Maybe there is a special way to solve integrals of this type?
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  2. #2
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    Re: Is this an improper integral?

    Nothing improper between the given limits:



    Any problems with the anti-derivative?
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  3. #3
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    Re: Is this an improper integral?

    Quote Originally Posted by infernalmich View Post
    I have to integrate Int(-1,1)(x2 ln(x+5))dx

    sorry for this way to write, but I didn't figure out the code to write it in proper form.

    This integral is improper because it's not defined for x<=-5.

    Is this true? How would you solve this integral in a fast way? I tried, but I always get stuck doing all the calculations. Can anyone give me some hint? Maybe there is a special way to solve integrals of this type?
    \int_{-1}^1 x^2 \ln(x+5) \, dx

    if one of the limits of integration were x = -5 , then it would be improper.

    as is, it's just a normal definite integral ... I would initially try integration by parts.
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  4. #4
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    Re: Is this an improper integral?

    Thank you for your help, now I remeber the definition that in order to be improper the indefinite values have to lie within the limits of integration.

    Another try:
    Int(1,2)(x/(12-x)1/3)dx

    This integral is improper because it is not defined for 1, which is inside of the limit of integration.

    In order to check if it is convergent, I set 1=b than I solve the integral and take its limit b->0+
    The limit exists and is finite, therefore the integral converges. True?
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  5. #5
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    Re: Is this an improper integral?

    true ... if the limit exists (I did not check if it indeed does so)
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