# How do you integrate #x^(-1/2) - sqrt(x) #?

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To integrate (x^{-1/2} - \sqrt{x}), you can break it into two separate integrals:

- For (x^{-1/2}), integrate using the power rule for integration, which states that ∫(x^n) dx = (\frac{x^{n+1}}{n+1}) + C:

∫(x^{-1/2}) dx = ( \frac{x^{(-1/2)+1}}{(-1/2)+1}) + C = ( \frac{2}{\sqrt{x}}) + C.

- For (-\sqrt{x}), use the power rule for integration:

∫(-\sqrt{x}) dx = (-\frac{2}{3}x^{3/2}) + C.

So, the integral of (x^{-1/2} - \sqrt{x}) is ( \frac{2}{\sqrt{x}} - \frac{2}{3}x^{3/2}) + C.

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