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Evaluate the Integral ∫8(x−1x2+2x)dx\int 8\left(\frac{x-1}{x^{2}+2 x}\right) d x A) 8(13x−13ln⁡x)+C8\left(\frac{1}{3} x-\frac{1}{3} \ln x\right)+C

Question 109

Multiple Choice

Evaluate the integral. ∫8(x−1x2+2x) dx\int 8\left(\frac{x-1}{x^{2}+2 x}\right) d x


A) 8(13x−13ln⁡x) +C8\left(\frac{1}{3} x-\frac{1}{3} \ln x\right) +C
B) −8(ln⁡x−x) +C-8(\ln x-x) +C
C) 8(32ln⁡(x+2) −12ln⁡x) +C8\left(\frac{3}{2} \ln (x+2) -\frac{1}{2} \ln x\right) +C
D) −8(22arctan⁡x) +C-8\left(\frac{\sqrt{2}}{2} \arctan x\right) +C
E)  None of these \text { None of these }

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