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Thread: Integration

  1. #1
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    Integration

    Integrate the following :-

    (3cos^2x+4sin^2x)/cos^2xsin^2x

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  2. #2
    Junior Member Cervesa's Avatar
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    Re: Integration

    If you meant $\cos^2{x}\sin^2{x}$ as the denominator of your expression, then

    $\displaystyle \int 3\csc^2{x} + 4\sec^2{x} \, dx = 4\tan{x}-3\cot{x} +C$

    should this integration problem be in the calculus forum?
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  3. #3
    MHF Contributor

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    Re: Integration

    First, of course, 3cos^2(x)+ 4sin^2(x)= 3cos^2(x)+ 3sin^2(x)+ sin^2(x)= 3(cos^2(x)+ sin^2(x))+ sin^2(x)= 3+ sin^2(x). And the denominator is cos^2(x)sijn^2(x)= (1- sin^2(x))sin^2(x)= sin^2(x)- sin^4(x).

    So the integrand can be written (3+ sin^2(x))/(sin^2(x)- sin^4(x)). Since those are all even powers of sin(x), I would use the identity sin^2(x)= (1- cos(2x))/2.
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