# How do you integrate #(x+3) / sqrt(x) dx#?

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To integrate ( \frac{x+3}{\sqrt{x}} ) with respect to ( x ), you can use substitution. Let ( u = \sqrt{x} ), then ( x = u^2 ) and ( du = \frac{1}{2\sqrt{x}}dx ). Substituting, the integral becomes:

[ \int \frac{x+3}{\sqrt{x}} , dx = \int \frac{u^2 + 3}{u} \cdot 2u , du ]

[ = \int (2u + \frac{3}{u}) , du ]

[ = \int 2u , du + \int \frac{3}{u} , du ]

[ = u^2 + 3\ln|u| + C ]

[ = x + 3\sqrt{x} + C ]

Where ( C ) is the constant of integration.

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