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Rewrite the fraction $\frac{\left(\sqrt{x}-1\right)^2}{3\sqrt{x}}$ inside the integral as the product of two functions: $\left(\sqrt{x}-1\right)^2\frac{1}{3\sqrt{x}}$
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$\int\left(\sqrt{x}-1\right)^2\frac{1}{3\sqrt{x}}dx$
Learn how to solve problems step by step online. Find the integral int(((x^1/2-1)^2)/(3x^1/2))dx. Rewrite the fraction \frac{\left(\sqrt{x}-1\right)^2}{3\sqrt{x}} inside the integral as the product of two functions: \left(\sqrt{x}-1\right)^2\frac{1}{3\sqrt{x}}. We can solve the integral \int\left(\sqrt{x}-1\right)^2\frac{1}{3\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.