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Math Help - [SOLVED] Trigonometric Integration Problem

  1. #1
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    [SOLVED] Trigonometric Integration Problem

    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by elven06 View Post
    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
    1- sin(2x)=2sin(x)cos(x).

    2- \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c} for c \neq 0.
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  3. #3
    Member mathemagister's Avatar
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    Quote Originally Posted by elven06 View Post
    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
    I've spent a lot of time on it and I could only go so far. I think it's option 4, but I can't see how. Maybe I need to brush up on logarithms. Sorry I wasn't able to go till the end, but I spent 40 minutes on this, and I thought I might as well tell you what I've got, or it would be a wasted 40 minutes.

    Hope this helps at least a little

    33 \int \frac{cos(x) + sin(x)}{sin(2x)}dx

    =33 \int \frac{cos(x)}{sin(2x)} + \frac{sin(x)}{sin(2x)}dx

    Use trig identity: sin(2x)=2sin(x)cos(x)

    =33 \int \frac{cos(x)}{2sin(x)cos(x)} + \frac{sin(x)}{2sin(x)cos(x)}dx

    =33 \int \frac{1}{2sin(x)} + \frac{1}{2cos(x)}dx

    =\frac{33}{2} \int \frac{1}{sin(x)} + \frac{1}{cos(x)}dx

    =\frac{33}{2} \int csc(x) + sec(x) dx

    I've just memorized the integrals of cosecant and secant, but they aren't too impossible to do.

    =\frac{33}{2} [-ln|cot(x)+csc(x)| + ln|tan(x) + sec(x)|]+C
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  4. #4
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    Thanks so much, it was in fact 4. The division step gave it away.
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