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:
D
`int(1+x-(1)/(x))e^((x+(1)/(x)))dx`
`=inte^((x+(1)/(x)))dx+intx(1-(1)/(x^(2)))e^((x+(1)/(x)))dx`
On integrating `intx(1-(1)/(x^(2)))e^((x+(1)/(x)))dx` by parts considering
x as first function and `(1-(1)/(x^(2)))e^((x+(1)/(x)))` as second function,
we get
`=inte^((x+(1)/(x)))dx+xe^((x+(1)/(x)))-inte^((x+(1)/(x)))dx`
`=xe^((x+(1)/(x)))+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|78 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 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