Final Answer
Step-by-step Solution
Specify the solving method
Expand the fraction $\frac{x^2-1}{\sqrt{2x-1}}$ into $2$ simpler fractions with common denominator $\sqrt{2x-1}$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{x^2}{\sqrt{2x-1}}+\frac{-1}{\sqrt{2x-1}}\right)dx$
Learn how to solve integrals of rational functions 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. The integral \int\frac{x^2}{\sqrt{2x-1}}dx results in: \frac{1}{20}\sqrt{\left(2x-1\right)^{5}}+\frac{1}{6}\sqrt{\left(2x-1\right)^{3}}+\frac{1}{4}\sqrt{2x-1}. Gather the results of all integrals.