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Math Help - Integration without Trig Sub

  1. #1
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    Red face Integration without Trig Sub

    How would I work the integral:
    x^3 * sqrt(x^2 -9) dx

    without using trig substitution? My professor said that it is a way, but I don't see it!
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  2. #2
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    Quote Originally Posted by latavee View Post
    How would I work the integral:
    x^3 * sqrt(x^2 -9) dx

    without using trig substitution? My professor said that it is a way, but I don't see it!
    Split the integrand up u=x^2, and dv=x\sqrt{x^2-9} \;dx then use integration by parts.

    CB
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  3. #3
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    THanks!

    AH! Never thought of that! Thank you!
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  4. #4
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    How about the substitution u=\surd(x^2-9) or equivalently x^2=u^2+9? Then x\,\mathrm dx=u\,\mathrm du and you end up with a polynomial in u to integrate.
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  5. #5
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    I would do \int x^3\sqrt{x^2- 9}dx by writing it as \int \left(x^2\sqrt{x^2-9}l\right)\left(xdx\right) and using the substitution u= x^2- 9. Then du= 2xdx so \frac{1}{2}du= xdx and x^2= u+ 9. That gives \int x^3\sqrt{x^2- 9}dx= \frac{1}{2}\int (u+ 9)\sqrt{u}du = \frac{1}{2}\int u^{3/2}+ 9u^{1/2} du
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  6. #6
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    I'm going to try some of these ideas out! and I will see if I can come up with the answer that I had using trig substitution/or nearly the same! Thanks guys!
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