試求下列第1題跟第3題各積分還有解法過程?

Sol
(1)
∫(0 to 1)_x√(x+2)dx
Set y=√(x+2)
y^2=x+2
dx=2ydy
∫(0 to 1)_x√(x+2)dx
=∫(√2 to √3)_(y^2－2)*y*2ydy
=∫(√2 to √3)_2y^4－4y^2dy
=2y^5/5－4y^3/3｜(√2 to √3)
=[(2/5)*3^(5/2)－(4/3)*3^(3/2)]－[(2/5)*2^(5/2)－(4/3)*2^(3/2)]
=[(18/5)*3^(1/2)－(4)*3^(1/2)]－[(8/5)*2^(1/2)－(8/3)*2^(1/2)]
=－(2/5)*3^(1/2)+(16/15)*2^(1/2)
=16√2/15－2√3/5
(3)
∫ln(√x)/xdx
Set y=√x
x-y^2
dx=2ydy
∫ln(√x)/xdx
=∫lny/(y^2)*2ydy
=2∫lny/ydy
=2∫lnydlny
=(lny)^2+c
=ln(√x)^2+c