Let `f(x)=e^(x)+2x+1` then find the value of `int_(2)^(e+3)f^(-1)(x)dx`

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

Evaluate: int_(-1)^(4)f(x)dx=4 and int_(2)^(4)(3-f(x))dx=7 then find the value of int_(2)^(-1)f(x)dx

Let f(x)=x+e^(x), thenvalue of int_(1)^(1+e)2f^(-1)(x)dx is equal to (where f^(-1)(x) denotes inverse of f(x))

If int_(0)^(1)e^(-(x^(2)))dx=a, then find the value of int_(0)^(1)x^(2)e^(-(x^(2)))dx in terms of a

If 2f(x)+f(-x)=(1)/(x)sin(x-(1)/(x)) then the value of int_((1)/(e))^(e)f(x)dx is

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Let f(x) be a continous function on R. If int_(0)^(1)[f(x)-f(2x)]dx=5 and int_(0)^(2)[f(x)-f(4x)]dx=10 then the value of int_(0)^(1)[f(x)-f(8x)]dx=

f(x)={:{(e-e^(x-[x]),, if [x] is odd), (e^(x-[x]),, if [x] is even):} ,then find the value of (2)/(e)int_(-3)^(3)f(x)dx

Let f(x)=x^(3)-3(x^(2))/(2)+x+(1)/(4) find the value of (int_((1)/(4))^((3)/(4))f(f(x))dx)^(-1)