Home
Class 12
MATHS
Evaluate: int(e^(2x)-2e^x)/(e^(2x)+1)dx...

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

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)log(e^(2x)+1)-2 tan^(-1)(e^(x))+C`
`int(e^(2x)-2e^(x))/(e^(2x)+1)dx=(1)/(2)int(2e^(2x))/(e^(2x)+1)dx-2int(e^(x)dx)/((e^(x))^(2)+1) `
`=(1)/(2)log(e^(2x)+1)-2int(dz)/(z^(2)+1), " where " z=e^(x) `
` =(1)/(2)log(e^(2x)+1)-2 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(e^(2x)-1)/(e^(2x)+1)dxdot

Evaluate int(e^(2x)+e^(-2x)+2)/(e^(x))

Evaluate: int(e^(3x)+e^(5x))/(e^x+e^(-x))dx

Evaluate int (e^(-x))/(16 + 9e^(-2x)) dx

Evaluate: inte^(xlog2)e^(x)dx

int(e^(x))/(e^(x)+1)dx= ……………

Evaluate int_0^1(e^x)/(1+e^(2x)) dx

int(e^x)/(e^(2x)+4)dx

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

Evaluate: int((x-1)e^x)/((x+1)^3)dx