Let f be a twice differentiable function on R and satisfying `f''(x)=(x^(2)+1)^((-3)/(2))AA x in R` .If f'(0)=0 and `f(1)=sqrt(2)+1` then `int_(0)^(1)f(x)dx`=

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

[" Let "f" be a twice differential function "],[" satisfying "(e^(x)f''(x)-e^(x)f'(x))/(e^(2x))=1" and "],[f(0)=0,f'(0)=1," then the value of "],[int_(0)^(1)(f(x))/(x)dx" is "]

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0 Then the value of f(9) is

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0, Then the value of f(9) is

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to