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welshfella

  • one year ago

Integrate cot x csc^2x dx

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  1. welshfella
    • one year ago
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    I'm trying the substitution u = cot x and using the identity csc^2 x = 1 + cot^2 x

  2. welshfella
    • one year ago
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    hold on its cot^x = 1 + csc^2 x right?

  3. anonymous
    • one year ago
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    \[\int\limits_{}^{}\cot x \csc ^2x dx=\int\limits_{}^{}\frac{ cosx }{ \sin^3x }dx\]

  4. welshfella
    • one year ago
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    and how would you proceed from there?

  5. amistre64
    • one year ago
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    if u = cot(x) what is du?

  6. anonymous
    • one year ago
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    u sub\[u=\sin x\]\[du=\cos x dx\]\[dx=\frac{ 1 }{ \cos x }\]

  7. welshfella
    • one year ago
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    du/dx ln sin x

  8. welshfella
    • one year ago
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    thats where i got stuck

  9. amistre64
    • one year ago
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    i recall D[tan(x)] = sec^2(x) D[cot(x)] = -csc^2(x)

  10. anonymous
    • one year ago
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    \[\int\limits_{}^{}\frac{ \cos x }{ u^3 }\frac{ 1 }{ \cos x }du\]

  11. amistre64
    • one year ago
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    \[\int cot(x)~csc^2(x)~dx\implies -\int u~du\]

  12. anonymous
    • one year ago
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    ya wanna take over am?

  13. welshfella
    • one year ago
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    ah - i was using ln sin x instead of -csc^2 x i can see it now

  14. amistre64
    • one year ago
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    take over? nah, just a perspective :)

  15. anonymous
    • one year ago
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    heh i have my own problems to solve too actually, not working too well

  16. amistre64
    • one year ago
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    welsh is a smart fella :)

  17. anonymous
    • one year ago
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    but i cant put it here cause it doesnt belong to maths

  18. welshfella
    • one year ago
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    yes I see it now thanks for your help

  19. welshfella
    • one year ago
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    I looked up the integral instead of the derivative!!!! that wasn't so smart!!!

  20. welshfella
    • one year ago
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    lol

  21. anonymous
    • one year ago
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    lol that happens alot

  22. welshfella
    • one year ago
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    ty both

  23. anonymous
    • one year ago
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    engineering department seems dead

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