Home
Class 12
MATHS
If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqr...

If `int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2log|g(x)|+c`, then-

A

f(x)=x+1

B

`f(x)=2(x-2)`

C

`g(x)=(sqrt(1+e^(x))-1)/(sqrt(1+e^(x))+1)`

D

`g(x)=(sqrt(1+e^(x))+1)/(sqrt(1+e^(x))-1)`

Text Solution

Verified by Experts

The correct Answer is:
A,C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTEGRATION BY PARTS

    CHHAYA PUBLICATION|Exercise Integer Answer Type|5 Videos

  • INTEGRATION BY PARTS

    CHHAYA PUBLICATION|Exercise Matrix Match Type|2 Videos

  • INTEGRATION BY PARTS

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|47 Videos

  • INTEGRALS OF SOME SPECIAL FORM OF FUNCTIONS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample questions for Competitive Exams ( D Comprehension Type)|4 Videos

Similar Questions

Explore conceptually related problems

int (e^(x)dx)/(sqrt(e^(x)+8))

int (e^(x)dx)/(sqrt(e^(2x)-a^(2)))

Knowledge Check

  • If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c , then

    A
    f(x) = x - 1
    B
    g(x) =`(sqrt(1+e^x) - 1)/(sqrt(1 + e^x) + 1)`
    C
    g(x) =`(sqrt(1+e^x) + 1)/(sqrt(1 + e^x) - 1)`
    D
    f(x) = 2(x - 2)

  • int (e^x (1+x))/(cos^2(xe^x)) dx is

    A
    `tan(xe^x)` + c
    B
    `tan^-1 (xe^x)` + c
    C
    `sqrttan(xe^x) + c`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Evaluate: inte^x/(sqrt(1-e^(2x)))dx

    int (log(x+1))/(sqrt(x+1))dx

    int (e^(x)dx)/(sqrt(e^(2x)-5e^(x)+6))

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

    int (e^(a sin^(-1)x))/(sqrt(1-x^(2)))dx

    Evaluate: int(e^x)/(sqrt(4-e^(2x)))\ dx

    Home
    Profile