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Math Help - Hard Integral Problem Involving an Inverse Trig Function

  1. #1
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    Hard Integral Problem Involving an Inverse Trig Function

    Hello! I was working with the volumes of regular spherical simplices and I came across these two integrals which I cannot solve. Please help me.

    1.
    Hard Integral Problem Involving an Inverse Trig Function-4.gif
    2.
    Hard Integral Problem Involving an Inverse Trig Function-5.gif
    I cannot find a way to calculate them. This is for my undergraduate thesis so I badly need it. Thanks!
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  2. #2
    Junior Member
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    Jul 2012
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    Jaipur,Rajasthan
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    Re: Hard Integral Problem Involving an Inverse Trig Function

    Hi,
    this is the question which can be solved by the method integration by parts. Integration by parts is technique which perform indefinite & definite integration by expanding the differential of a product of functions and expressing the original integral in terms of a known integral. It is particularly used in the functions having algebraic, trigonometry, logarithmic expressions etc. Now, for your question I gave you a hint to start the question,
    Let us suppose, sec^-1(1+z)=t & 1/((3+z)(sqrt(3+z^2)-1))dz = dt
    thus we have to do the integration of , t*dt
    Now find the integration of t separately. Such that,
    (1+z)=sint
    d(1+z)=costdt
    I=(integration of)(sinttdt)
    I=(integration of)(tsintdt)

    Now you can solve the remaining steps easily I think by integrating & putting the values.
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