Evaluate ∫ 4x2-3x/(x-2)(x2+1)dx

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Evaluate ∫ 4x2-3x/(x-2)(x2+1)dx

 

Answer No.1

Anonymous

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Step 1: Partial fraction expansion. The expression you have can be written as 2x/(x^2+1) +1/(x^2+1) + 2/(x-2). For the first, set x^2+1 =u, then xdx=du/2. So we need the integralof du/u = ln u = ln|x2+1| For the second, this is a standard integral, its just arctan(x) For the third, this is just 2 ln|x-2| Add these together to get ln|x2+1|+arctan(x) +2 ln|x-2|+c.

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