Find
∫x2e2x dx \int x^2e^{2x} \, dx ∫x2e2xdxUse the substitution u=2x+1u = \sqrt{2x + 1}u=2x+1 to show that
∫12x2x+1 dx=2(2x+1)12(Ax+B)+k \int \frac{12x}{\sqrt{2x + 1}} \, dx = 2(2x + 1)^{\frac{1}{2}}(Ax + B) + k ∫2x+112xdx=2(2x+1)21(Ax+B)+kwhere AAA and BBB are integers to be found and kkk is an arbitrary constant.
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.
