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.
MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th Pass

                        

1.∫(e 200x +e 202x)/ (e x +e -x )dx. 2.∫e x [(2-sin2x)/(1-cos2x)]dx 3.∫[x 5 ]/[(x 2 +x+1)(x 6 +1)(x 4 -x 3 +x-1)]dx 4.∫[x 3 +2x 2 +x+2]/[(x 2 +1) 1/2 ]dx 5. ∫dx/(5-13sinx) 6.∫dx/(a 2 -b 2 cos 2 x) a 2 >b 2

8 years ago

Answers : (1)

Jitender Singh
IIT Delhi
askIITians Faculty
158 Points
							
Ans:
I = \int \frac{e^{200x} + e^{202x}}{e^{x}+e^{-x}}dx
I = \int e^{201x}dx = \frac{e^{201x}}{201} + constant
I = \int e^{x}.\frac{2-sin2x}{1-cos2x}dx
I = \int e^{x}.\frac{2-2sinx.cosx}{2sin^{2}x}dx
I = \int e^{x}.(csc^{2}x - cotx)dx
I = \int -e^{x}.(cotx-csc^{2}x)dx
I = -\int (e^{x}.cotx)'dx = -e^{x}.cotx + constant
I = \int \frac{x^{5}}{(x^{2}+x+1)(x^{6}+1)(x^{4}-x^{3}+x^{2}-1)}
Simply using the partial fraction here, we have
I = \frac{1}{12}(log(\frac{1-x^{6}}{1+x^{6}})) + constant
I = \frac{1}{6}tanh^{-1}(x^{6}) + constant
I = \int \frac{x^{3}+2x^{2}+x+1}{\sqrt{x^{2}+1}}dx
t = tanx
dt = sec^{2}x.dx
I = \int (sect+tan^{3}t.sect+2tan^{2}t.sect+sect.tant)dt
I = \frac{sec^{3}t}{3}+sect.tant + constant
I = \frac{1}{3}\sqrt{x^{2}+1}(x^{2}+3x+1)+constant
I = \int \frac{1}{5-13sinx}dx
t = tan(\frac{x}{2})
dt = \frac{1}{2}sec^{2}(\frac{x}{2})dx
I = 2\int \frac{1}{5t^{2}-26t+5}dt
I = \frac{1}{6}tanh^{-1}(\frac{1}{12}(13-5t)) + constant
I = \frac{1}{6}tanh^{-1}(\frac{1}{12}(13-5tan(\frac{x}{2}))) + constant
I = \int \frac{1}{a^{2}-b^{2}cos^{2}x}dx
I = \int \frac{sec^{2}x}{a^{2}sec^{2}x-b^{2}}dx
I = \int \frac{sec^{2}x}{a^{2}+a^{2}tan^{2}x-b^{2}}dx
t = tanx
dt = sec^{2}xdx
I = \int \frac{1}{a^{2}+a^{2}t^{2}-b^{2}}dt
I = \frac{1}{a^{2}-b^{2}}\int \frac{1}{\frac{a^{2}t^{2}}{a^{2}-b^{2}}+1}dt
I = \frac{tan^{-1}(\frac{at}{\sqrt{a^{2}-b^{2}}})}{a\sqrt{a^{2}-b^{2}}} + constant
I = \frac{tan^{-1}(\frac{atanx}{\sqrt{a^{2}-b^{2}}})}{a\sqrt{a^{2}-b^{2}}} + constant
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


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