Find
∫e2xex+1 dx \int \frac{e^{2x}}{\sqrt{e^x + 1}} \, dx ∫ex+1e2xdxDuring 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 0 dtdm=3t+427t,t≥0Use 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)+kwhere AAA and BBB are integers to be found and kkk is a constant of integration.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
