[int(|x|)/(x)dx," where "a<0

If int_(0)^(x)[x]dx=int_(0)^(|x|)x dx, (where [.] and {.} denotes the greatest integer and fractional part respectively), then

where c is the constant of integration and m,n in N ,the find the valuc of (m+n). If int(dx)/(1+sqrt(x+1)+sqrt(x))=ax+b sqrt(x)+c int sqrt((x+1)/(x))dx where a,b,care constant,then find the value of (a+b+c)

int_a^(b) |x|/x dx, (Where 0 lt a lt b) =

If I_(n) = int x^(n)e^(x) dx where n inN , then I_(n) + nI_(n-1) =

If f(x) is a polynomial of nth degree then int e^(x)f(x)dx= Where f^(n)(x) denotes nth order derivative of f(x)w.r.t.x

If f(x) =(e^(x))/(1+e^(x)),I_(1)=overset(f(a))underset(f(-a))int xg{x(1-x)}dx and I_(2)=overset(f(a))underset(f(-a))int g{x(1-x)}dx , where g is not identify function. Then the value of I_(2)//I_(1) , is

Property 12:int_(a)^(a+nT)f(x)dx=n int_(0)^(T)f(x)dx where T is period of f(x)