Home
Class 12
MATHS
Evaluate: int1/(e^x+e^(-x))\ dx...

Evaluate: `int1/(e^x+e^(-x))\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`tan^(-1)(e^(x))+C`
`I=int(dx)/(e^(x)+e^(-x))=int(e^(x)dx)/(e^(2x)+1)`
Let `e^(x)=t.`
` :. e^(x)dx=dt`
` :. I=int(dt)/(t^(2)+1)=tan^(-1)t+C=tan^(-1)(e^(x))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.3|16 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

Evaluate: int(1)/(e^(x)+e^(-x))dx

Evaluate: int(1)/(1+e^(-x))dx

Evaluate: int(1)/(e^(x)+1)dx

Evaluate: int(1)/(1+e^(-x))dx

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

Evaluate: int1/(2\ e^(2x)+3\ e^x+1)\ dx

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

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

Evaluate: int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx

Evaluate: int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx