Express $\frac{4-5x}{2+x-x^2}$ in partial fractions. Hence, integrate \(\displaystyle\displaystyle

Question

Express $\frac{4-5x}{2+x-x^2}$ in partial fractions. Hence, integrate $\displaystyle\displaystyle \displaystyle\int_{0}^{1} \frac{4-5x}{2+x-x^2} \, \mathrm{d}x$

Accepted Answer

$\frac{4-5x}{2+x-x^2}=-\frac2{2-x}+\frac3{x+1}$; hence $\int_0^1\frac{4-5x}{2+x-x^2}\,\mathrm dx=\ln2$

Integration - Problems involving Partial Fractions

Integration - Problems involving Partial Fractions

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