# ∫cot^3(x) dx

• Durum: Closed
• Ödül: \$10
• Alınan Girdiler: 23
• Kazanan: apeterpan52

## Yarışma Özeti

∫cot^3(x) dx
Please provide the best way of descripting. Thank you.

Winner

## İşveren Geribildirimi

“Very good job!”

hendry071, Indonesia.

## Genel Açıklama Panosu

• Yarışma Sahibi
• 3 yıl önce

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

• 3 yıl önce
1. ###### trinhngochai1
• 3 yıl önce

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 ;))

• 3 yıl önce
2. Yarışma Sahibi
• 3 yıl önce

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.

• 3 yıl önce
• ###### matlab53
• 3 yıl önce

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

• 3 yıl önce
• ###### MohamedJoe
• 3 yıl önce

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

• 3 yıl önce
• ###### amaghazi1984
• 3 yıl önce

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)