Home
Class 12
MATHS
int(dx)/(sqrt(2e^(x)-1))=...

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

A

`2sec^(-1)sqrt(2e^(x))+c`

B

`-2"tan"^(-1)(1)/(sqrt(2e^(x)-1))+c`

C

`2sec^(-1)(sqrt(2)e^(x))+c`

D

`2tan^(-1)sqrt(2e^(x)-1)+c`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`I=int(dx)/(sqrt(2e^(x)-1))`
`"Let " 2e^(x)-1=t^(2)`
` :. 2e^(x)dx=2t dt`
` :. I=int(t dt)/((t^(2)+1)/(2)*t)`
`=2tan^(-1)t+C`
`=2tan^(-1)sqrt(2e^(x)-1)+C`
`=-2"tan"^(-1)(1)/(sqrt(2e^(x)-1))+C`
`"Also, " tan^(-1)sqrt(2e^(x)-1)=sec^(-1)sqrt(2e^(x))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

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

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

Knowledge Check

  • int(dx)/(sqrt(1-e^(2x)))=?

    A
    `log |e^(x)+sqrt(e^(2x)-1)|+C`
    B
    `log |e^(-x)+sqrt(e^(-2x)-1)|+C`
    C
    `-log |e^(-x)+sqrt(e^(-2x)-1)|+C`
    D
    None of these

  • int(e^(x))/(sqrt(e^(2x)-1))dx=

    A
    `sin^(-1)(e^(x))+c`
    B
    `log(e^(x)-sqrt(e^(2x)-1))+c`
    C
    `log(e^(x)+sqrt(e^(2x)-1))+c`
    D
    `sec^(-1)(e^(x))+c`

  • int(dx)/(sqrt(1-e^(2x))) is equal to

    A
    `log|e^(-x)+sqrt(e^(-2x)-1)|+c`
    B
    `log|e^(x)+sqrt(e^(2x)-1)|+c`
    C
    `-log|e^(-x)+sqrte^(-2x)-1)|+c`
    D
    `-log|e^(-2x)+sqrt(e^(-2x)-1)|+c`

    • Similar Questions

    Explore conceptually related problems

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

    int(dx)/(e^(x)sqrt(2e^(x)-1))=2sec^(-1)sqrt(2e^(x))+c-2tan^(-1)(1)/(sqrt(2e-1))+c2sec^(-1)(sqrt(2)e^(x))+c(d)2tan^(-1)sqrt(2e^(x)-1)+c

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

    int(e^(x))/(sqrt(1+e^(x)))dx=?

    int(e^(5x))/(sqrt(e^(5x)+1))dx=

    Home
    Profile