Integrate $ \frac{x^2-\sqrt{x}}{x} $ with respect to x

Assessment: JAMB UTME - Mathematics - 2007 Subject: General Mathematics

Question 1 Report

\frac{x^{2} - \sqrt{x}}{x^{2}}

+ k

\frac{x^{2}}{2}

-

\sqrt{x}

+ k

\frac{2 (x^{2} - x)}{3 x}

+ k

\frac{x^{2}}{2}

- 2

\sqrt{x}

+ k

Answer Details

Integrate $\frac{x^{2} - \sqrt{x}}{x}$ with respect to x
∫ $\frac{x^{2} - \sqrt{x}}{x}$ dx = ∫( $\frac{x^{2}}{x} - \frac{\sqrt{x}}{x}$ )dx
= ∫(x - x $\frac{1}{2}$ )dx
= $\frac{x^{2}}{2}$ - $\frac{x^{\frac{1}{2}}}{\frac{1}{2}}$ + k
= $\frac{x^{2}}{2}$ - 2 $\sqrt{x}$ + k