Home
Class 12
MATHS
inte^(x)((1+xlogx)/(x))dx=?...

`inte^(x)((1+xlogx)/(x))dx=?`

A

`e^(x)*(1)/(x)+C`

B

`e^(x)logx+C`

C

`xe^(x)logx+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=inte^(x)((1)/(x)+logx)dx`
`=inte^(x){f(x)+f'(x)}dx" where"f(x)=logx`
`=e^(x)f(x)+C=e^(x)logx+C`.
Promotional Banner

Topper's Solved these Questions

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Exercise 13C|87 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5F|21 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29 B|2 Videos

Similar Questions

Explore conceptually related problems

int(e^(x)(1+xlogx))/(x)dx=

inte^(x)((x-1)/(x^(2)))dx=

int_(1)^(e)e^(x)((1+xlogx)/(x))dx

int e^x ((1+xlogx)/x)dx=e^x (mlog x) +c , then m=

inte^(x)*(x)/((1+x)^(2))dx=?

int x^(x) (1+ log x) dx

Evaluate: int(e^x(1+xlogx))/xdx

int(1)/(xlogx(2+logx))dx=

int(e^(x))/((1+x)^(3))dx-int(e^(x))/(2(1+x)^(2))dx=

int(1)/(x(1+log x))dx