how do u find the antiderivative of (xto the power of 1/2) + (1/2 times the square root of x)????

Answer 1

∫x^(1/2)+(1/2) x^(1/2) dx
= ∫(3/2) x^(1/2) dx
= x^(3/2) + c

Answer 2

x^(1/2) + (1/2)x^(1/2) = (3/2)x^(1/2)
∫(3/2)x^(1/2) =
(2/3)(3/2)x^(3/2) + C =
x^(3/2) + C

Answer 3

an antiderivative is also an integral and x to the 1/2 is the squareroot of x. the integral of that is (2/3)*x^(3/2). the whole thing therefore is (2/3)*x^3/2 + (1/3)*x^3/2 or x^3/2 +c