Final Answer
$\frac{1}{2}x^2+2x+\frac{1}{2}\ln\left(x^2-2x+2\right)+C_0$
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Step-by-step Solution
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1
Simplifying
$\int\frac{x^3-x+3}{x^2-2x+2}dx$
Learn how to solve differential equations problems step by step online.
$\int\frac{x^3-x+3}{x^2-2x+2}dx$
Learn how to solve differential equations problems step by step online. Find the integral int((x^3-x+3)/(x^2+1*-2x+2))dx. Simplifying. Divide x^3-x+3 by x^2-2x+2. Resulting polynomial. Expand the integral \int\left(x+2+\frac{x-1}{x^2-2x+2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final Answer
$\frac{1}{2}x^2+2x+\frac{1}{2}\ln\left(x^2-2x+2\right)+C_0$