Determine constants $A, B, C$ such that $$\frac{2x^{2}+3x-5}{(x-1)(x^{2}+4)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+4}.$$ Then evaluate the definite integral $$I=\int_{0}^{2}\frac{2x^{2}+3x-5}{(x-1)(x^{2}+4)}\,dx.$$

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$A=0,\;B=2,\;C=5;\;I=\ln 2+\frac{5\pi}{8}$

Neco 2017 Further Mathematics Question 27

Determine constants \(A, B, C\) such that \[\frac{2x^{2}+3x-5}{(x-1)(x^{2}+4)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+4}.\] Then evaluate the definite integral \[I=\int_{0}^{2}\frac{2x^{2}+3x-5}{(x-1)(x^{2}+4)}\,dx.\]

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