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

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

A

`e^x + c`

B

`e^x log x + c`

C

`e^x/x + c`

D

`log x + c`

Text Solution

Verified by Experts

The correct Answer is:
`e^x log x + c`
I = int(e^x(logx+1/x)dx) Using Integration by parts on e^x log x int(e^x log x) = log x int(e^x) - int(d(logx)/dx(int(e^x)) int(e^x log x) = e^x log x + c - int(1/x*e^x) Adding this value of int(e^x log x) in I I = e^x log x + c - int(1/x*e^x) +int(1/x*e^x) I = e^x log x + c
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Knowledge Check

  • inte^(x)(logx+1/x)dx is equal to :

    A
    `e^(x)+c`
    B
    `e^(x)logx+c`
    C
    `e^(x)/x+c`
    D
    `logx+c`

  • int e^(log x)/x dx =

    A
    `log x+c`
    B
    `e^logx+c`
    C
    `xlog x +c`
    D
    `xe^logx+c`

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