I have two questions I need help with. I have attempted both of them but I have no idea how to proceed from here.

Question 1:

Attempted solution:

I used product rule then I solved for d/dx of the integral but I have no idea how to solve for the integral in the first term of my final equation.

Question 2:

Attempted solution:

The question gave a hint: "Rewrite it as lim_n-> infinity 1/n(*) then relate what you get to a Riemann sum. I got it to the point where I got the 1/n term out of the sum but I have no idea what the formula for the sum of a square root is and I can't find it anywhere.

I'm not looking for the full solution I just want to know if I did so far is correct and how to continue further.

Thanks in advance