3.90: Integral of rational function

0606/21/O/N/23 — Question 3 · 6 marks

(a)
Find ∫(4x+5−12x+3) dx\displaystyle\int\left(4x+5-\dfrac{1}{2x+3}\right)\,\mathrm{d}x.
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(b)
Hence find the exact value of ∫13(4x+5−12x+3) dx\displaystyle\int_{1}^{3}\left(4x+5-\dfrac{1}{2x+3}\right)\,\mathrm{d}x, simplifying your answer.
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