Explain why it is not possible to find the value of \(\int_{-3}^1 \frac{3x^2+3x+3}{(x+2)(x-1)^2}\,dx\).[2]
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Answer:(a) \(\dfrac1{x+2}+\dfrac2{x-1}+\dfrac3{(x-1)^2}\). (b) \(\ln(28/5)+3/4\approx2.47\) (3 s.f.). (c) The improper integral diverges: it has non-integrable poles at \(x=-2\) and \(x=1\).