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Math Help - help with integration!

  1. #1
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    help with integration!

    Really need help! How do I integrate 4/(sqrt(x)sqrt(1-x)) and e^(-x)cosx? I tried using algebraic manipulation for the first one and integration by parts for the second, got a mess of workings, really will appreciate your help!
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  2. #2
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    Re: help with integration!

    Hey Tutu.

    Try using the fact that SQRT(x)*SQRT(1-x) = SQRT(x - x^2) and then complete the square.

    Hint: Completing the square for ax^2 + bx is adding the term (0.5*b/SQRT(a))^2 and also -(0.5*b/SQRT(a))^2 to get (SQRT(a)*x + 0.5*b/SQRT(a))^2 - (0.5*b/SQRT(a))^2.
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    Re: help with integration!

    Thanks! Couof you help ke with also the second one, thanks so much!
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    Re: help with integration!

    For the second on try integration by parts by integrating the the trigonometric term twice (in other words do by parts twice) and then collect terms.
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    Re: help with integration!

    Solution for the second integral is given in the attached sheet.
    Be careful in selecting the first and second function while integrating by parts.
    help with integration!-integration-parts.png
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  6. #6
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    Re: help with integration!

    Hi thanks a lot for both your help! I am confused though, according to the LIATE rule,
    u should be cos(x) since trigo functions come before exponential, isn't it?
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  7. #7
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    Re: help with integration!

    In this case it won't make any difference, as exponential functions only change by a constant multiple when differentiated or integrated, and sine and cosine functions repeat each other by constant multiples after being differentiated or integrated twice.
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