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Math Help - Integral problems

  1. #1
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    Integral problems

    I have 2 problems:


    Integral problems-problem1.gif What to use for substitute?

    Integral problems-problem2.gif
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  2. #2
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    Re: Integral problems

    The first, use integration by parts, integrating the trig function so that the x 'disappears' when differentiated. To integrate the fraction, sub u = cos x, or better still see it (the fraction) as a chain-rule derivative (spotting sin as the inner derivative), or else re-write as tan x sec x, as here,

    integrate x sin x / cos^2 x - Wolfram|Alpha

    For sec itself, see Balloon Calculus: standard integrals, derivatives and methods #sec

    The second is more usually written cot (for cotangent). Apply a reduction formula as here,

    integrate ctg^7 x - Wolfram|Alpha

    or develop your own, using \cot^2 x \equiv 1 + \csc^2 x, and doing integration by parts on

    \csc^2 x \cot^5 x ...
    Last edited by tom@ballooncalculus; July 1st 2012 at 05:50 AM.
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  3. #3
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    Re: Integral problems

    Thanks a lot!
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