Express $\dfrac{7x^2+6x+2}{(x+1)^2(2x-1)}$ in partial fractions.[3] Hence evaluate the exact value

Question

Express $\dfrac{7x^2+6x+2}{(x+1)^2(2x-1)}$ in partial fractions.[3] Hence evaluate the exact value of $\displaystyle\int_1^2 \dfrac{7x^2+6x+2}{(x+1)^2(2x-1)}\,\mathrm{d}x$.[4]

Accepted Answer

(i) $\dfrac2{x+1}-\dfrac1{(x+1)^2}+\dfrac3{2x-1}$ (ii) $\dfrac72\ln3-2\ln2-\dfrac16$

Repeated linear factors and an exact integral

Repeated linear factors and an exact integral

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