Integrate (frac{x^2 -sqrt{x}}{x}) with respect to x
-
A.
(frac{x^2}{2}-2sqrt{x}+K) -
B.
(frac{2(x^2 – x)}{3x}+K) -
C.
(frac{x^2}{2}-sqrt{x}+K) -
D.
(frac{(x^2 – x)}{3x}+K)
Correct Answer: Option A
Explanation
(int frac{x^2 -sqrt{x}}{x} = int frac{x^2}{x} – frac{x^{frac{1}{2}}}{x}\
int x – x^{frac{-1}{2}}\
=left(frac{1}{2}right)x^2 – frac{x^{frac{1}{2}}}{frac{1}{2}}+K\
=frac{x^2}{2}-2x^{frac{1}{2}}+K\
=frac{x^2}{2}-2sqrt{x}+K)