MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Shraddhey Srivastava Grade: 12
        

Integrate 


sin x dx /sin 5x


&


1 dx / (sin5x+cos5 x) 

7 years ago

Answers : (1)

Jitender Singh
IIT Delhi
askIITians Faculty
158 Points
										
Ans:
I = \int \frac{sinx}{sin5x}dx
I = \int sinx.cosec5x.dx
Simplify it using trigonometry identity, we have
I = \int \frac{sec^{4}x}{2+2sec^{2}x+sec^{4}x-12tan^{2}x-2sec^{2}x.tan^{2}x+2tan^{4}x}dxtanx = t
sec^{2}x.dx = dt
I = \int \frac{t^{2}+1}{t^{4}-10t^{2}+5}dt
I = \int (\frac{\sqrt{5}-3}{2\sqrt{5}(t^{2}+2\sqrt{5}-5)}+\frac{-3-\sqrt{5}}{2\sqrt{5}(-t^{2}+2\sqrt{5}+5})dt
I =\frac{ (\sqrt{5+\sqrt{5}})tanh^{-1}(\frac{(\sqrt{5}-3)t}{\sqrt{10-2\sqrt{5}}})+(\sqrt{5-\sqrt{5}})tanh^{-1}(\frac{(3+\sqrt{5})t}{\sqrt{10+2\sqrt{5}}})}{5\sqrt{2}}+cons
I =\frac{ (\sqrt{5+\sqrt{5}})tanh^{-1}(\frac{(\sqrt{5}-3)tanx}{\sqrt{10-2\sqrt{5}}})+(\sqrt{5-\sqrt{5}})tanh^{-1}(\frac{(3+\sqrt{5})tanx}{\sqrt{10+2\sqrt{5}}})}{5\sqrt{2}}+cons
Second integrand is not clear.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

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