Final Answer
$\frac{1}{2}x^2+2x-\frac{5}{2}\ln\left(\frac{\frac{\sqrt{2}}{2}}{\sqrt{\frac{1}{2}+\left(x-1\right)^2}}\right)-\frac{\sqrt{2}}{2}\arctan\left(1.414201\left(x-1\right)\right)+C_0$
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Step-by-step Solution
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1
Take out the constant $2$ from the integral
$2\int\frac{x^3}{2x^2-4x+3}dx$
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$2\int\frac{x^3}{2x^2-4x+3}dx$
Learn how to solve problems step by step online. Find the integral int((2x^3)/(2x^2-4x+3))dx. Take out the constant 2 from the integral. Divide x^3 by 2x^2-4x+3. Resulting polynomial. Expand the integral \int\left(\frac{1}{2}x+1+\frac{\frac{5}{2}x-3}{2x^2-4x+3}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final Answer
$\frac{1}{2}x^2+2x-\frac{5}{2}\ln\left(\frac{\frac{\sqrt{2}}{2}}{\sqrt{\frac{1}{2}+\left(x-1\right)^2}}\right)-\frac{\sqrt{2}}{2}\arctan\left(1.414201\left(x-1\right)\right)+C_0$