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Math Help - Integration problem, stuck, not sure

  1. #1
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    Integration problem, stuck, not sure

    Hello,
    Covering the topic of Indefinite Integral:

    I am doing a question, which my book does not give the answer and hoping someone can look at it and tell me if I did this right.

    Integre/sign then ( x^2 + 4x + 4 ) ^ 1/3 dx

    So I worked out 1/3 to the numbers in the brackets.
    So I have Int Sign ( x^7/3 + 4 x^4/3 + 4^1/3)
    then:
    int sign x^7/3 dx + 4 intsign x^4/3 dx + 4^1/3 intsign dx
    So my answer is
    3/10 x^10/2 + 12/7 x^7/3 + 4^1/3 x + C.


    is this correct? or not, thanks.
    Joanne
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  2. #2
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    Re: Integration problem, stuck, not sure

    Hi Brady,
    So I worked out 1/3 to the numbers in the brackets.
    So I have Int Sign ( x^7/3 + 4 x^4/3 + 4^1/3)
    This is wrong as a polynomial cannot be broken down the way you have assumed it to.

    This is how you can go about doing it x^2 + 4x + 4 = (x+2)^2 so you are expected to evaluate
    \int{((x+2)^2})^{\frac{1}{3}}dx} \Rightarrow \int{(x+2)^{\frac{2}{3}} dx} substitute t= x+2 and finish you integral.

    Kalyan
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  3. #3
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    Re: Integration problem, stuck, not sure

    So is the answer
    3/5(x+2)^5/3 + C ??

    Thanks for the help, and correcting me as well.
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  4. #4
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    Re: Integration problem, stuck, not sure

    Quote Originally Posted by bradycat View Post
    So is the answer
    3/5(x+2)^5/3 + C ??

    Thanks for the help, and correcting me as well.
    check the validity of an antiderivative by taking the derivative of your solution ...
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  5. #5
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    Re: Integration problem, stuck, not sure

    Oh I forgot about that, ya it's correct then.
    Thanks
    Joanne
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