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Math Help - integration

  1. #1
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    integration

    could you please help me to find the solution

    {integrat from 0 to 1} (x^n) /(x+5) dx
    integrat from 0 to 1} (x^(n+1) )/(x+5) dx
    I think we have to use integration by parts but how many times or there is another way
    I appreciate any help
    Thank you all
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  2. #2
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    Use long division.
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  3. #3
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    what do you mean by long division?
    using several integration by parts
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  4. #4
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    Review partial fractions.
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  5. #5
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    Quote Originally Posted by koko2009 View Post
    could you please help me to find the solution

    {integrat from 0 to 1} (x^n) /(x+5) dx
    integrat from 0 to 1} (x^(n+1) )/(x+5) dx
    I think we have to use integration by parts but how many times or there is another way
    I appreciate any help
    Thank you all
    I suggest you first consider simple concrete cases like n = 0, 1 and 2. Then you might make better sense of the help you have been given and see why integration by parts is not going to be much help.
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  6. #6
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    Let u= x+ 5 and then use the Binomial expansion of (u- 5)^n.
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