Use algebraic integration and the substitution u=xu = \sqrt{x}u=x to find the exact value of ∫1963x+xx dx\int_{1}^{9} \frac{6}{3x + x\sqrt{x}} \, dx∫193x+xx6dx Write your answer in the form 4ln(ab)4 \ln \left(\frac{a}{b}\right)4ln(ba), where aaa and bbb are integers to be found. (Solutions relying entirely on calculator technology are not acceptable.)
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.