In a chemical reactor, the rate of accumulation of a byproduct, MMM grams per hour, is given by the function R(t)=203+2t+1R(t) = \frac{20}{3 + \sqrt{2t + 1}}R(t)=3+2t+120, where ttt is the time in hours since the reaction started. The total mass produced between t=0t = 0t=0 and t=12t = 12t=12 is given by
∫012203+2t+1 dt\int_{0}^{12} \frac{20}{3 + \sqrt{2t + 1}} \, dt∫0123+2t+120dt
Using the substitution u=3+2t+1u = 3 + \sqrt{2t + 1}u=3+2t+1, find the exact mass produced, giving your answer in the form a+blnca + b \ln ca+blnc, where aaa, bbb, and ccc are integers.
Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.