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Math Help - Another Integral Problem

  1. #1
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    Another Integral Problem

    Integral from Pi/4 to Pi/3 of ln(tanx)dx/sinxcosx

    I know 2sinxcosx = sin2x, but does this even help? Derivative of tanx = sec^2x = 1/cos^2x but I don't think this helps either. Any help/advice?

    Thanks!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Let u =ln(tan(x))

    Then after calculating du convert to sines and cosines and everything will cancel nicely
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  3. #3
    Member courteous's Avatar
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    Hello Sprintz!

    First use a variable substitution: u=\log\tan(x) \Rightarrow du=\frac{1}{\sin(x)\cos(x)}dx
    Then insert back into the integral and cancel out and get (mind the changed integration boundaries): \int_0^{\log\sqrt{3}}udu=\frac{u^2}{2}\big|_0^{\lo  g\sqrt{3}}=\frac{1}{2}(\log\sqrt{3})^2
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  4. #4
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    Hmm kind of embarrassing that I couldn't get that eh? Is it a matter of simply memorizing these derivatives and integrals? I have a test tomorrow (hence the review problems) and will have to know all of them.

    Any tips to do so? My memory is really lacking. Is it a matter of doing the same types of problem enough to gain familiarity?

    I've exhausted all of the problems in my textbook. Does anyone know if there is a website that generates Integral problems, or a list somewhere of problems that I can look over? I find this to be the most efficient method of review.

    Cheers
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  5. #5
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    Have you tried deriving the derivatives and integrals for tangent, cotangent, cosecant, secant and natural log?
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