Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{4}}{4}+x^{3}-6x+8\ln\left(\frac{\sqrt{\frac{11}{4}}}{\sqrt{\frac{11}{4}+\left(x-\frac{1}{2}\right)^2}}\right)+\frac{439}{52}\arctan\left(0.6030246x-\frac{60}{199}\right)+C_0$
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Step-by-step Solution
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Find the integral
$\int\frac{x^6+5x^4+3x^2-2x}{x^2-x+3}dx$
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$\int\frac{x^6+5x^4+3x^2-2x}{x^2-x+3}dx$
Learn how to solve problems step by step online. Find the integral of (x^6+5x^43x^2-2x)/(x^2-x+3). Find the integral. Divide x^6+5x^4+3x^2-2x by x^2-x+3. Resulting polynomial. Expand the integral \int\left(x^{4}+x^{3}+3x^{2}-6+\frac{-8x+18}{x^2-x+3}\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{4}}{4}+x^{3}-6x+8\ln\left(\frac{\sqrt{\frac{11}{4}}}{\sqrt{\frac{11}{4}+\left(x-\frac{1}{2}\right)^2}}\right)+\frac{439}{52}\arctan\left(0.6030246x-\frac{60}{199}\right)+C_0$