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Rewrite the fraction $\frac{\left(\sqrt{x}+3\right)^2}{2\sqrt{x}}$ inside the integral as the product of two functions: $\left(\sqrt{x}+3\right)^2\frac{1}{2\sqrt{x}}$
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$\int_{4}^{9}\left(\sqrt{x}+3\right)^2\frac{1}{2\sqrt{x}}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function ((x^1/2+3)^2)/(2x^1/2) from 4 to 9. Rewrite the fraction \frac{\left(\sqrt{x}+3\right)^2}{2\sqrt{x}} inside the integral as the product of two functions: \left(\sqrt{x}+3\right)^2\frac{1}{2\sqrt{x}}. We can solve the integral \int\left(\sqrt{x}+3\right)^2\frac{1}{2\sqrt{x}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.