Express 3x−3(x+1)(2x−1)\displaystyle \frac{3x - 3}{(x + 1)(2x - 1)}(x+1)(2x−1)3x−3 in partial fractions
Given that x>1x > 1x>1, find the general solution to the differential equation
(x+1)(2x−1)dydx=y(3x−3) (x + 1)(2x - 1) \frac{dy}{dx} = y(3x - 3) (x+1)(2x−1)dxdy=y(3x−3)Hence find the particular solution to the differential equation that satisfies y=6y = 6y=6 at x=5x = 5x=5, giving your answer in the form y=f(x)y = f(x)y=f(x)
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.