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Math Help - Integration

  1. #1
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    Integration

    Can anyone help me find the intergral of this, need to know how for my workshop in a couple of hours.

    X+1/(1+x^2)^3/2 dx

    I tried substitution but didn't get far, any help?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    This is \int{\frac{x}{\left( 1+x^{2} \right)^{3/2}}\,dx}+\int{\frac{dx}{\left( 1+x^{2} \right)^{3/2}}}.

    The first integral is easy, just put u^2=1+x^2. As for the second one, you can perform the standard trigonometric substitution x=\tan\varphi.
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  3. #3
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    Can you explain to me how the tan part works please?
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  4. #4
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    It x= tan(t), then 1+ t^2= 1+ tan^2(t)= sec^2(t) so that \sqrt{1+ t^2}= sec(t) and du= sec^2(t)dt.
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