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1 Pure Mathematics

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Question 94
a.

Given that

2x2−x+1x+1≡Ax+B+Cx+1\displaystyle \frac{2x^2 - x + 1}{x + 1} \equiv Ax + B + \frac{C}{x + 1}x+12x2−x+1​≡Ax+B+x+1C​, x≠−1x \neq -1x=−1

find the values of the constants AAA, B B\,B and CCC.

[3]
b.

Hence, using algebraic integration, find the exact value of

∫072x2−x+1x+1 dx\displaystyle\int_0^7 \frac{2x^2 - x + 1}{x + 1}\,dx∫07​x+12x2−x+1​dx

giving your answer in the form a+bln⁡2a + b\ln 2a+bln2, where a a\,a and b b\,b are integers to be found.

[4]
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1 Pure Mathematics Questions

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