Question

why is the integral of sqrtx = 2x^(3/2)/3 and not just x^(3/2)/3

Answer 1

try to convert the radical form to exponent form using the formula :

\[ \sqrt[n]{x^{m}} = x^{m/n}\]

Answer 2

then find the deravative using the deravative of power x rule , that is \[ d/dx(x^{n})= n x^{n-1}\]

Answer 3

in your question \[\sqrt{x}=x^{1/2}\] ===> \[ d/dx(\sqrt{x}) = d/dx(x^{1/2}) = 1/2(x^{-2/3} )= 1/2x^{2/3}\]

Answer 4

hope that helps