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Integrate partial fractions with logarithm and arctangent terms

Using partial fractions, find ∫029x2+x−13(2x−5)(x2+9) dx\displaystyle\int_0^2\frac{9x^2+x-13}{(2x-5)(x^2+9)}\,dx. Give your answer as aln⁡b+ctan⁡−1da\ln b+c\tan^{-1}d, with rational a,b,c,da,b,c,d.

[2014/II/2]

CJC · Discussion · Question 2

Separate the linear denominator from the irreducible quadratic, then split the quadratic numerator.

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