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Question
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
Sum
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Solution
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}}dx\]
\[ = \int \left( \frac{x^2 - 2x + x - 2}{\sqrt{x}} \right)dx\]
`=∫((x^2-x-2)/sqrt(x))dx`
\[ = \int\left( x^\frac{3}{2} - x^\frac{1}{2} - 2 x^{- \frac{1}{2}} \right)dx\]
\[ = \left[ \frac{x^\frac{3}{2} + 1}{\frac{3}{2} + 1} \right] - \left[ \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} \right] - 2\left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = \frac{2}{5} x^\frac{5}{2} - \frac{2}{3} x^\frac{3}{2} - 4 x^\frac{1}{2} + C\]
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