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Math Help - cot integral

  1. #1
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    Question cot integral

    Hi,

    Can someone help me with the integral Cot/sq. 1+2sinx, please?

    I tried doing u substitution

    I set u=1+sinx
    du=2cosx

    Will this work or should I try integration by parts?

    I also know that cot=1/tan

    Thank you
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chocolatelover View Post
    Hi,

    Can someone help me with the integral Cot/sq. 1+2sinx, please?

    I tried doing u substitution

    I set u=1+sinx
    du=2cosx

    Will this work or should I try integration by parts?

    I also know that cot=1/tan

    Thank you
    you cannot have cot by itself, you have to have cot(something). please type your question properly
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  3. #3
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    Sorry

    Cotx/sq. 1+2sinx
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  4. #4
    MHF Contributor red_dog's Avatar
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    \displaystyle\int\frac{\cot x}{(1+2\sin x)^2}dx=\int\frac{\cos x}{\sin x(1+2\sin x)^2}dx
    Substitute \sin x=u.
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  5. #5
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    I'm trying to integrate "Cotx/sq. 1+2sinx"

    Can someone please help me?

    Thank you
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chocolatelover View Post
    Sorry

    Cotx/sq. 1+2sinx
    and by that i suppose you mean \frac {\cot x}{\sqrt{1 + 2sin(x)}} ?

    parentheses are important too. change cot(x) into cos(x)/sin(x), then make the substitution u = \sqrt {1 + 2 \sin x}
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  7. #7
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    Would the final answer be 1/2ln sq. 1+2sinx+c

    I did:

    (1/2) int du/sq. u dx=
    1/2 int. 1/sq. u dx
    1/2 int. ln|sq. u|+c=
    1/2 ln sq. 1+2sinx+c

    Thank you
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chocolatelover View Post
    Would the final answer be 1/2ln sq. 1+2sinx+c

    I did:

    (1/2) int du/sq. u dx=
    1/2 int. 1/sq. u dx
    1/2 int. ln|sq. u|+c=
    1/2 ln sq. 1+2sinx+c

    Thank you
    please read my instructions in my last post, and use parentheses to clarify what you mean
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  9. #9
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    Quote Originally Posted by chocolatelover View Post
    Can someone help me with the integral Cot/sq. 1+2sinx, please?
    Does this make sense?

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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    Does this make sense?

    Hey, it's the same question (asked by the same person). I saw that thread but i didn't remember it, since i never posted in it. i made the same substitution as you did
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