Mathematics

Integrate (frac{x^2 -sqrt{x}}{x}) with respect to x

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)