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How to solve this problem- - Integral Calculus - JEE Main-8

Evaluate \int e^{x/2}(lnx +2/x)dx

  • Option 1)

    2e^{x/2}lnx + C

  • Option 2)

    (e^{x/2}lnx)/2 + C

  • Option 3)

    e^{x/2}lnx/2 + C

  • Option 4)

    2e^{x/2}lnx/2 + C

 
Answers (1)
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S subam

As we have learned

Result for integration by parts -

\int e^{ax} \left (f(x)+\frac{f'(x)}{a}dx\right ) = \frac{e^{ax}f(x)}{a}+c

 

- wherein

Put ax=t 

dx=\frac{dt}{a}

 

 I= \int e^{x/2}(lnx +2/x)dx

I= \int e^{x/2}(lnx +\frac{d/dx(lnx)}{x/2})dx

I={2e^{x/2}lnx } + C 

 

 

 

 


Option 1)

2e^{x/2}lnx + C

Option 2)

(e^{x/2}lnx)/2 + C

Option 3)

e^{x/2}lnx/2 + C

Option 4)

2e^{x/2}lnx/2 + C

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