# How do you integrate #int (sqrtx+1/(2sqrtx))dx#?

First, make the equation simpler.

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To integrate ( \int \left(\sqrt{x} + \frac{1}{2\sqrt{x}}\right) , dx ), use the formula for integrating each term separately.

For ( \int \sqrt{x} , dx ), use the power rule for integration. [ \int \sqrt{x} , dx = \frac{2}{3}x^{\frac{3}{2}} + C ]

For ( \int \frac{1}{2\sqrt{x}} , dx ), rewrite ( \frac{1}{2\sqrt{x}} ) as ( \frac{1}{2}x^{-\frac{1}{2}} ) and then use the power rule for integration. [ \int \frac{1}{2\sqrt{x}} , dx = \int \frac{1}{2}x^{-\frac{1}{2}} , dx = x^{\frac{1}{2}} + C ]

So, the integral ( \int \left(\sqrt{x} + \frac{1}{2\sqrt{x}}\right) , dx ) becomes: [ \frac{2}{3}x^{\frac{3}{2}} + x^{\frac{1}{2}} + C ]

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