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Take the constant $\frac{1}{3}$ out of the integral
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$\frac{1}{3}\int\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}dx$
Learn how to solve differential calculus problems step by step online. Find the integral int(((x^1/2-1)^2)/(3x^1/2))dx. Take the constant \frac{1}{3} out of the integral. Rewrite the integrand \frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}} in expanded form. Expand the integral \int\left(\frac{x}{\sqrt{x}}-2+\frac{1}{\sqrt{x}}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Simplify the fraction by x.