Given that 2x2−x+1x+1≡Ax+B+Cx+1x≠−1\displaystyle \frac{2x^2 - x + 1}{x + 1} \equiv Ax + B + \frac{C}{x + 1} \quad x \neq -1x+12x2−x+1≡Ax+B+x+1Cx=−1
find the values of the constants AAA, B B\,B and CCC.
Hence, using algebraic integration, find the exact value of
∫012x2−x+1x+1dx \int_0^1 \frac{2x^2 - x + 1}{x + 1} dx ∫01x+12x2−x+1dxgiving your answer in the form a+bln2a + b \ln 2a+bln2 where a a\,a and b b\,b are integers to be found.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.