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Math Help - Two problems with integrals.

  1. #1
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    Two problems with integrals.

    I'm having difficulties with a few homework problems.

    The first one I need to use u substitution to evaluate the definite integral on [-pi/2, pi/2] for ((x^2 * sinx)/(1 + x^6))dx

    I'm just lost as to where to use the substitution, if anyone has some pointers that'd be great.

    The other problem I'm supposed to evaluate the integral using logarithmic differentiation on the [e,6] for dx/xlnx

    Same problem with this one, I just don't know where to begin with it.

    Thanks for any advice/help!
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  2. #2
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    Quote Originally Posted by WolfMV View Post
    I'm having difficulties with a few homework problems.

    The first one I need to use u substitution to evaluate the definite integral on [-pi/2, pi/2] for ((x^2 * sinx)/(1 + x^6))dx

    I'm just lost as to where to use the substitution, if anyone has some pointers that'd be great.

    The other problem I'm supposed to evaluate the integral using logarithmic differentiation on the [e,6] for dx/xlnx

    Same problem with this one, I just don't know where to begin with it.

    Thanks for any advice/help!
    If f(x) is odd on [-a,a] then \int_{-a}^a f(x)\,dx = 0 and f(x) = \frac{x^2 \sin x}{1+x^6} is odd on [-\frac{\pi}{2}, \frac{\pi}{2}]. For the second problem, try u = \ln x.
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