14. int frac{x^{2}+1}{x-2} d x= (A) x+2+frac{5}{x-2}+C (B) frac{x^{2}}{2}+2 x+frac{5 x}{frac{x^{2}}{2}-2 x}+C (C) frac{x^{2}}{2}+2 x+5 ln |x-2|+C (D) frac{frac{x^{3}}{3}+x}{frac{x^{2}}{2}-2 x}+C
Added by Lizeth D.
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First, we can divide the integral into two parts: \( \int \frac{x^{2}+1}{x-2} d x = \int \frac{x^{2}}{x-2} dx + \int \frac{1}{x-2} dx \) For the first part, we can use polynomial division to simplify the integrand: \( \frac{x^{2}}{x-2} = x - 2 + \frac{4}{x-2} Show more…
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