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Math Help - Integration question

  1. #1
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    Integration question

    Hi
    Can someone tell me how would i anti-differentiate the following:
    1) \frac{x}{x+1}
    2) In this question you have to evaluate the following definite integrals:
    This is what i done:
    \int_1^5e+\frac{1}{x}dx
    =e^x+ln(x)
    =e^5+ln^5-e^1+ln(1)
    =ln(5)+e^4

    answer was ln(5) +4e but i don't understand how they got it.

    P.S
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Paymemoney View Post
    Hi
    Can someone tell me how would i anti-differentiate the following:
    1) \frac{x}{x+1}
    Hint: \frac{x}{x+1}=1-\frac{1}{x+1}

    2) In this question you have to evaluate the following definite integrals:
    This is what i done:
    \int_1^5e+\frac{1}{x}dx
    =e^x+ln(x)
    =e^5+ln^5-e^1+ln(1)
    =ln(5)+e^4

    answer was ln(5) +4e but i don't understand how they got it.

    P.S
    \int e\,dx\neq e^x. Here, e is a constant; this means we apply the rule \int a\,dx=ax+C.

    Also, e^5-e^1\neq e^4. You can't subtract the exponents like that.
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  3. #3
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    ok i understand why it is 4e now thanks.
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  4. #4
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    Just be make sure i am right, for 1) do you divide x by x+1? or divide x+1 by x?
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  5. #5
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    Quote Originally Posted by Paymemoney View Post
    Just be make sure i am right, for 1) do you divide x by x+1? or divide x+1 by x?
    you divide x by x+1. use polynomial long division. or since these are simple and easy polynomials, you can use a little trick. what i do is add and subtract a 1 from the top so you have (x + 1 - 1) / (x + 1), then i rearrange: (x+1)/(x+1) - (1/(x+1)) so now the integrand becomes 1 - (1/(x+1))
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