Home
Class 12
MATHS
The integral int(1+x-1/x)e^(x+1/x)dx is ...

The integral `int(1+x-1/x)e^(x+1/x)dx` is equal to

A

`(x-1)e^(x+(1)/(x))+c`

B

`xe^(x+(1)/(x))+c`

C

`(x+1)e^(x+(1)/(x))+c`

D

`-xe^(x+(1)/(x))+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(1+x-(1)/(x))e^((x+(1)/(x)))dx`
`=int e^((x+(1)/(x)))dx+int x(1-(1)/(x^(2)))e^((x+(1)/(x)))dx+c`
`=int e^((x+(1)/(x)))dx+xe^((x+(1)/(x)))-int e^((x+(1)/(x)))dx+c`
`" "`(integrating second integral using by parts)
`=xe^((x+(1)/(x)))+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Single Correct Answer Type|48 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Numerical)|10 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

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to: (Here C is a constant of integration)

The integral int(2)/(e^(2x)-1)dx is equal to (Here C is a constant of integration)

int1/(1+e^(x))dx is equal to

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

int(1)/(e^(x)+1)dx is equal to

int(1)/(e^(x)+1)dx is equal to

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

int(1+x)/(x+e^(-x))dx is equal to