Home
Class 12
MATHS
If I=int(e^x)/(e^(4x)+e^(2e)+1) dx. J=in...

If `I=int(e^x)/(e^(4x)+e^(2e)+1) dx. J=int(e^(-x))/(e^(-4x)+e^(-2x)+1) dx.` Then for an arbitrary constant c, the value of `J-I` equal to

A

`(1)/(2)log|(e^(4x)-e^(2x)+1)/(e^(4x)+e^(x)+1)|+C`

B

`(1)/(2)log|(e^(2x)+e^(x)+1)/(e^(2x)-e^(x)+1)|+C`

C

`(1)/(2)log|(e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1)|+C`

D

`(1)/(2)log|(e^(4x)-e^(2x)+1)/(e^(4x)+e^(2x)+1)|+C`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS.AIEEE/JEE MAIN PAPERS|35 Videos

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|8 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS |3 Videos

Similar Questions

Explore conceptually related problems

Let I =int(e^(x))/(e^(4x)+e^(2x)+1)dx , J = int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx . Then for an arbitary constant C, the value of I - J equals

I=int(e^x)/(e^(x)-1)dx

int(e^(x)dx)/(e^(x)-1)

int(e^(-x))/(1+e^(x))dx=

I = int(dx)/(e^(x) + 4.e^(-x)) dx =

int(e^(x))/((1+e^(x))(2+e^(x)))dx

int(e^(4x)-1)/(e^(2x))dx

int(e^(x))/((e^(x)-1)(e^(x)+2))dx=

int(dx)/(e^(x)+4e^(-x))=