Statement-I: int (x+1)/(x(1+xe^(x))^(2))...

Statement-I: `int (x+1)/(x(1+xe^(x))^(2))dx=(1)/(1+xe^(x))+log |(xe^(x))/(1+ xe^(x))|+c` where c is a real number.
Statement-II: `(d)/(dx)(xe^(x))=(x+1)e^(x).`

Statement-I is True, Statement-II is True, Statement-II is a correct explanation for Statement-I

Statement-I is True, Statement-II is True, Statement-II is not a correct explanation for Statement-I

Statement-I is True, Statement-II is False.

Statement-I is False, Statement-II is True.

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The correct Answer is:

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If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2log|g(x)|+c , then-

f(x)=x+1

`f(x)=2(x-2)`

`g(x)=(sqrt(1+e^(x))-1)/(sqrt(1+e^(x))+1)`

`g(x)=(sqrt(1+e^(x))+1)/(sqrt(1+e^(x))-1)`