Assertion (A) :`int(e^(x))/(x) (1 + x log x) dx = e^(x) log x +c`. Reason (R) :`int e^(x) [f(x) + f'(x)] dx = e^(x) f(x) + c`

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

B

Explanation

Consider `int (e^(x))/(x) (1 + x log x) dx`
`= int (e^(x))/(x) dx + int e^(x) log x dx`
`= e^(x) log x - int e^(x) log x dx + int e^(x) log x dx = e^(x) log x`
(R) `int e^(x) [f(x) + f'(x)] dx`
`= int e^(x) f(x) dx + int e^(x) f'(x) dx`
`= e^(x) f(x) - int e^(x) f'(x) dx + int e^(x) f'(x) dx = e^(x) f(x) + c`
Both A and R are true but R is not the correct explanation of A