N2014 P2 Q2
N2014 P2 Q2
Junior College 2
9 marks
Use partial fractions to find \[\int_0^2\frac{9x^2+x-13}{(2x-5)(x^2+9)}\,\mathrm dx,\] giving your answer in the form \(a\ln b+c\tan^{-1}d\), where \(a\), \(b\), \(c\) and \(d\) are rational numbers.[9]
Solution:
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Answer:\(\frac32\ln\frac{13}{45}+\frac83\tan^{-1}\frac23\).
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