Jambmaths question:
Integrate $\frac{{{x}^{2}}-\sqrt{x}}{x}$ with respect x
Option A:
$\frac{2({{x}^{2}}-x)}{3x}+k$
Option B:
$\frac{{{x}^{2}}-\sqrt{x}}{{{x}^{2}}}+k$
Option C:
$\frac{{{x}^{2}}}{2}-2\sqrt{x}+k$
Option D:
$\frac{{{x}^{2}}}{2}-\sqrt{x}+k$
Jamb Maths Solution:
$\begin{align} & \int{\frac{{{x}^{2}}-\sqrt{x}}{x}}dx=\int{\left( \frac{{{x}^{2}}}{x}-\frac{\sqrt{x}}{x} \right)dx} \\ & =\int{(x-{{x}^{-\tfrac{1}{2}}})dx} \\ & =\frac{{{x}^{2}}}{2}-2{{x}^{\tfrac{1}{2}}}+k \\ & =\frac{{{x}^{2}}}{2}-2\sqrt{x}+k \end{align}$
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