Question

Solve the Integril ( intleft(sqrt{x}+frac{1}{sqrt{x}}right)^{2} d x )

( intleft(sqrt{x}+frac{1}{sqrt{x}}right)^{2} d x )

Solution

( intleft(sqrt{x}+frac{1}{sqrt{x}}right)^{2} d x=intleft(x+frac{1}{x}+frac{2 sqrt{x}}{sqrt{x}}right) d x )

( =intleft(x+frac{1}{x}+2right) d x )

( =frac{x^{2}}{2}+log _{e} x+2 x+6 )