badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
Close

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass 

                        
integration [(sin^3 X)/{(1+cos^2 X)(sqrt(1+cos^2 X+cos^4 X))}]=?

							
integration [(sin^3 X)/{(1+cos^2 X)(sqrt(1+cos^2 X+cos^4 X))}]=?
6 years ago

Answers : (1)

Sumit Majumdar
IIT Delhi
askIITians Faculty
137 Points 
							
Solution:
Let u=cos(x),
Then the required intergral would be given by:
\int \frac{sin^{3}x}{\left ( 1+cos^{2}x \right )\left ( \sqrt{1+cos^{2}x+cos^{4}x} \right )}=\int \frac{u^{2}-1}{\left ( 1+u^{2} \right )\left ( \sqrt{1+u^{2}+u^{4}} \right )}=\int \frac{1}{\sqrt{1+u^{2}+u^{4}}}-2\int \frac{1}{\left ( 1+u^{2} \right )\sqrt{1+u^{2}+u^{4}}}The second integral can further be simpified as follows:
2\int \frac{1}{\left ( 1+u^{2} \right )\sqrt{1+u^{2}+u^{4}}}=2\int \frac{1}{\left ( 1+u^{2} \right )\sqrt{\left ( u^{2}+\frac{1}{2} \right )^{2}+\frac{3}{4}}}
Now using the standard formulae, the final result can be arrived at.


Thanks & Regards



Sumit Majumdar,



askIITians Faculty



Ph.D,IIT Delhi
6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Integral Calculus

{ ( cos ^-1x { √(1-x^2) }]^-1) ÷ ( log e { 1 + ( sin(2x√(1-x^2)) ÷ 2) }) dx Answer & Earn Cool Goodies
Find the integral of a function having intervals 1 to 0 and the function f(x)=x^7/2.(1-x)^5/2dx Answer & Earn Cool Goodies
Please solve the question in the image attached Answer of this question is Option 2
Question 19.i am not able to get the proper answer.can you please help me?
Please solve the question in the image attached...........with appropriate solution...
View all Questions »


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers To Win!!! Click Here for details