`int(x+1)/(x(1+x e^x)^2)dx=log|1-f(x)|+f(x)+c`, then `f(x)=`

STATEMENT-1 : If int(1)/(f(x))dx=2log|f(x)|+c , then f(x)=(x)/(2) . STATEMENT-2 : When f(x)=(x)/(2) , then int(1)/(f(x))dx=int(2)/(x)dx=2log|x|+c STATEMENT-3 : inte^(x^(2))dx=e^(x^(2))+c

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c , then (a) f(x) is an even function (b) f(x) is a bounded function (c) the range of f(x) is (0,1) (d) f(x) has two points of extrema

If int(1)/(x^(2)+2x+2)dx=f (x) +C , then f (x)=

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

f(x) = int(x^(2)+x+1)/(x+1+sqrt(x))dx , then f(1) =

If int((x-1)/(x^2))e^x dx=f(x)e^x+c , then write the value of f(x) .

If int((x-1)/(x^2))e^x\ dx=f(x)\ e^x+C , then write the value of f(x) .

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

If 3f(x)-f((1)/(x))= log_(e) x^(4) for x gt 0 ,then f(e^(x))=

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=