Show that $\frac{5x^2 + 10x + 7}{x^2 + 2x + 1} = 5 + \frac{2}{(x + 1)^2}$. Hence find \(\disp

Question

Show that $\frac{5x^2 + 10x + 7}{x^2 + 2x + 1} = 5 + \frac{2}{(x + 1)^2}$. Hence find $\displaystyle\displaystyle\int_{-10}^{-5} \frac{5x^2 + 10x + 7}{x^2 + 2x + 1} \ \mathrm{d}x$.

Accepted Answer

(a) Shown; (b) $\dfrac{455}{18}$

Techniques of Integration - Integration by Splitting the Numerator

Techniques of Integration - Integration by Splitting the Numerator

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