∫cot^3(x) dx

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  • Hadiah: $10
  • Penyertaan diterima: 23
  • Pemenang: apeterpan52

Ringkasan Peraduan

∫cot^3(x) dx
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  • hendry071
    Penganjur Peraduan
    • 2 tahun yang lalu

    Thank you for all of your work. The winner I chose provided me a complete explanations. Thank you so much. :)

    • 2 tahun yang lalu
    1. trinhngochai1
      trinhngochai1
      • 2 tahun yang lalu

      Congratulations to apeterpan52! It is a great entry and a great contest. I would like to request that if you don't mind give a review to the other freelancers that were great and didn't won (including myself) it would only take u 15 min and it would be greatly appreciated. I think you just go to our profiles and talk good about us ;))

      • 2 tahun yang lalu
    2. hendry071
      Penganjur Peraduan
      • 2 tahun yang lalu

      Thank you so much for your entry :). I have gone to your profile page but I can't put a review for you. I suggest only the winner could get that buddy. :) Once again, thank you for your effort, I appreciate it a lot.

      • 2 tahun yang lalu
  • matlab53
    matlab53
    • 2 tahun yang lalu

    http://postimg.org/image/gibdfk2zb/

    • 2 tahun yang lalu
  • MohamedJoe
    MohamedJoe
    • 2 tahun yang lalu

    hi .. here is my answer ..check it , if there is mistakes or u can not understand any thing with this soluation
    ∫cot^3(x) dx=
    ∫cot^2(x) . cot(x) dx =∫cot(x) . (csc^2(x) - 1) dx =
    -∫-cot(x) .csc^2(x)dx -∫cot(x) dx =
    -(csc^3(x))/3 -∫(cos(x))/(sin(x)) dx =
    -(csc^3(x))/3 + ln (sin(x)) + C

    • 2 tahun yang lalu
  • amaghazi1984
    amaghazi1984
    • 2 tahun yang lalu

    Use Trigonometric Identities: cot2x=csc2x−1
    ∫(csc2x−1)cotxdx

    2 Expand (csc2x−1)cotx
    ∫cotxcsc2x−cotxdx

    3 Apply the Sum Rule: ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx
    ∫cotxcsc2xdx−∫cotxdx

    4 Simplify the trig functions
    ∫cosxsin3xdx−∫cotxdx

    5 Apply Integration By Substitution to ∫cosxsin3xdx
    Let u=sinx, du=cosxdx

    6 Using u and du above, rewrite ∫cosxsin3xdx
    ∫1u3du

    7 Apply the Power Rule: ∫xndx=xn+1n+1+C
    −12u2

    8 Substitute u=sinx back into the original integral
    −12sin2x

    9 Rewrite the integral with the completed substitution
    −12sin2x−∫cotxdx

    10 The integral of cotx is ln(sinx)
    −12sin2x−ln(sinx)

    11 Add constant
    −12sin2x−ln(sinx)+C

    • 2 tahun yang lalu

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