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Expand the fraction $\frac{x^2-1}{\sqrt{2x-1}}$ into $2$ simpler fractions with common denominator $\sqrt{2x-1}$
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$\int\left(\frac{x^2}{\sqrt{2x-1}}+\frac{-1}{\sqrt{2x-1}}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x^2-1)/((2x-1)^1/2))dx. Expand the fraction \frac{x^2-1}{\sqrt{2x-1}} into 2 simpler fractions with common denominator \sqrt{2x-1}. Expand the integral \int\left(\frac{x^2}{\sqrt{2x-1}}+\frac{-1}{\sqrt{2x-1}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the fraction \frac{x^2}{\sqrt{2x-1}} inside the integral as the product of two functions: x^2\frac{1}{\sqrt{2x-1}}. We can solve the integral \int x^2\frac{1}{\sqrt{2x-1}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.