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Math Help - indefinate integral x/(x+2)^1/4

  1. #1
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    indefinate integral x/(x+2)^1/4

    When I work at this I get it as being 4[(x+2)^3/4 ] / 3 + C Is this correct?
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  2. #2
    Super Member PaulRS's Avatar
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    mmmm, no, you forgot something there

    \int\frac{x}{(x+2)^{1/4}}dx=\int\frac{x+2-2}{(x+2)^{1/4}}dx=\int(x+2)^{3/4}dx-2\int(x+2)^{-1/4}dx

    \int(x+2)^{3/4}dx=\frac{4}{7}\cdot{(x+2)^{7/4}}+k_1

    \int(x+2)^{-1/4}dx=\frac{4}{3}\cdot{(x+2)^{3/4}}+k_2

    Thus: \int\frac{x}{(x+2)^{1/4}}dx=\frac{4}{7}\cdot{(x+2)^{7/4}}-\frac{8}{3}\cdot{(x+2)^{3/4}}+k
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  3. #3
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    Thanks PaulRS but how/why do you get x+2-2 on the numerator ?
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  4. #4
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    Quote Originally Posted by Craka View Post
    Thanks PaulRS but how/why do you get x+2-2 on the numerator ?
    Note that x + 2 - 2 = x. It is done to facilitate breaking the integral up into two more obvious integrals. As an alternative, you could make the substitution u = x + 2 and go from there.

    By the way, you can check an answer to an integal by differentiating it and seeing whether the result is equal to the integrand.
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