Question

What is the integral of a square root? Please explain.

Answer 1

if y = xⁿ

∫y dx =  xⁿ⁺¹ / (n + 1)  +  C    Provided n ≠ -1.

y = √x

y = x^(0.5)

∫y dx  =  x^(0.5+1) / (0.5 + 1) =   x^(1.5)  / 1.5 = x^(1.5)  / (3/2)

∫y dx = (2/3) x^(1.5)  + C.

∫y dx = (2/3) x^(3/2)  + C.

∫y dx = (2/3)√x³  + C

Answer 2

Its not guaranteed to be same form.it could be any polynomial that can not be easily formed into squares .try one out!