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Math Help - integral with improper fraction

  1. #1
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    integral with improper fraction

    The integral of x^3/\sqrt(1+x)

    How do you start this integral since it is an improper fraction. I tried squaring the top and bottom, but that didn't seem to work. What else should I try
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    Quote Originally Posted by stevo970 View Post
    The integral of x^3/\sqrt(1+x)

    How do you start this integral since it is an improper fraction. I tried squaring the top and bottom, but that didn't seem to work. What else should I try
    A substitution. Let u^2 = 1 + x

    Can you finish?
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    correction x^3/\sqrt(1+x^2)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stevo970 View Post
    correction x^3/\sqrt(1+x^2)
    That's even better! we won't have to cube a binomial.

    Similar approach, let u^2 = 1 + x^2
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    so would you then have to figure out

    du= x/\sqrt(1+x^2)dx or is that not the next step
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stevo970 View Post
    so would you then have to figure out

    du= x/\sqrt(1+x^2)dx or is that not the next step
    That's not the next step...

    u^2 = 1 + x^2 \implies \boxed{x^2 = u^2 - 1}

    \Rightarrow 2u~du = 2x~dx

    \Rightarrow u~du = x~dx

    Now substitute and finish up
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