# OCR A Level: Core 4 - Partial Fractions [January 2013 Q10]

Calculus Level 4

$$(\text{i})$$ Use algebraic division to express $$\dfrac{x^3-2x^2-4x+13}{x^2-x-6}$$ in the form $$Ax+B+\dfrac{Cx+D}{x^2-x-6}$$, where $$A$$, $$B$$, $$C$$ and $$D$$ are constants.

$$(\text{ii})$$ Hence find $\large \int _{ 4 }^{ 6 }{ \frac { x^{ 3 }-2x^{ 2 }-4x+13 }{ x^{ 2 }-x-6 } } \, dx$ giving your answer in the form $$a+ \ln b$$.

Input $$ab$$ as your answer.

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