Find ∫e2xex+1 dx\int \frac{e^{2x}}{\sqrt{e^x + 1}} \, dx∫ex+1e2xdx
During a chemical reaction, the rate of change of the mass mmm of a byproduct, in grams per hour, is modeled by the equation dmdt=27t3t+4,t≥0\frac{dm}{dt} = \frac{27t}{\sqrt{3t + 4}}, \quad t \ge 0dtdm=3t+427t,t≥0 Use the substitution u=3t+4u = \sqrt{3t + 4}u=3t+4 to show that ∫27t3t+4 dt=2(3t+4)12(At+B)+k\int \frac{27t}{\sqrt{3t + 4}} \, dt = 2(3t + 4)^{\frac{1}{2}}(At + B) + k∫3t+427tdt=2(3t+4)21(At+B)+k where AAA and BBB are integers to be found and kkk is a constant of integration.
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.