If `int_a^x ty(t)dt=x^2+y(x),` then find `y(x)`

If int_(0)^(x^(2)(1+x))f(t)dt = x then find f(2)

f(x)=int_(log ex)^(x)(dt)/(x+t), then find f'(x)

A curve passing through (2,3) and satisfying the differential equation int_(0)^(x)ty(t)dt=x^(2)y(x),(x>0) is

Let f(x) = int_(0)^(x)(t-1)(t-2)^(2) dt , then find a point of minimum.

For x in x!=0, if y(x) differential function such that x int_(1)^(x)y(t)dt=(x+1)int_(1)^(x)ty(t)dt then y(x) equals: (where C is a constant.)

For x in R, x != 0 if y(x) is a differentiable function such that x int_(1)^(x)y(t)dt = (x+1) int_(1)^(x)ty(t)dt , then y(x) equals (where C is a constant)

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If y = int_(4)^(4x^(2))t^(4)e^(4t)dt , find (d^(2)y)/(dx^(2))