Final Answer
$4\ln\left(\sqrt{2-x^2}\right)-x+\frac{3\sqrt{2}}{2}\ln\left(\frac{x+\sqrt{2}}{x-\sqrt{2}}\right)+C_1$
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Step-by-step Solution
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$\int\frac{4-4x+x^2}{2-x^2}dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\frac{4-4x+x^2}{2-x^2}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(((2-x)^2)/(2-x^2))dx. Expand. Divide 4-4x+x^2 by 2-x^2. Resulting polynomial. Expand the integral \int\left(-1+\frac{-4x+6}{2-x^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final Answer
$4\ln\left(\sqrt{2-x^2}\right)-x+\frac{3\sqrt{2}}{2}\ln\left(\frac{x+\sqrt{2}}{x-\sqrt{2}}\right)+C_1$