Recent content by algebrist

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    Techniques for Integrating the Cotangent Function

    well, I'm always rediscovering the wheel you know... :smile:
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    Techniques for Integrating the Cotangent Function

    anyway... i see your point i just wanted to do it in a more straight-forward fashion because this antiderivative business seems artificial to me... with your logic you can just learn by heart the derivatives of infinitely many functions and never use any technique of integration except for...
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    Techniques for Integrating the Cotangent Function

    but my problem is that i can't integrate 1/sin^2 well, it must be possible to derive it by just knowing the derivatives of sin and cos only. i tried integration by parts but it would'n work
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    Techniques for Integrating the Cotangent Function

    as i told you i don't find Integral of 1/sin(x)^2 dx an easy one
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    Techniques for Integrating the Cotangent Function

    but i would like to know how this antiderivative is obtained
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    Techniques for Integrating the Cotangent Function

    ahhh i see...
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    Techniques for Integrating the Cotangent Function

    ok the antiderivative of cosec^2 = -cot so how do i use it?
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    Techniques for Integrating the Cotangent Function

    ha-ha-ha do you imply that i just have to know the result by heart? what i am asking is how to solve Integral of cot(x)^2 dx i know the result, i want to know how to obtain it i have tried integration by parts and trigonometric identities but nothing seems to work
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    Techniques for Integrating the Cotangent Function

    why should i care about cot's derivative? i don't see your point
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    Techniques for Integrating the Cotangent Function

    hmm well, of course i get cot(x)^2 when i differentiate... the question is how do i solve the integral without knowing that it's equal to -x - cot(x) if i use cos(x)^2 + sin(x)^2 == 1 i get to solve Integral of 1/sin(x)^2 dx which i don't find easier
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    Techniques for Integrating the Cotangent Function

    well, can somebody please tell me how do i get that: Integral of cot(x)^2 dx == -x - cot(x) what technique of integration should be used here?
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    What is the structure of group algebras for D4 and Q8?

    group algebras of D4 and Q8.. please help! ok this is my problem: --------------------------------------------------------------------- for D4 - the dihedral group of order 8 and Q8 - quaternion group of order 8 describe the group algebra kG (for a big enough k so that Masche thm...
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