Express $\dfrac{3x^2+3x+6}{x(x+1)(x+3)}$ in partial fractions.[3] Hence evaluate \(\displaystyle\i

Question

Express $\dfrac{3x^2+3x+6}{x(x+1)(x+3)}$ in partial fractions.[3] Hence evaluate $\displaystyle\int_1^2 \dfrac{3x^2+3x+6}{x(x+1)(x+3)}\,\mathrm{d}x$, giving your answer as a single logarithm.[4]

Accepted Answer

(i) $\dfrac2x-\dfrac3{x+1}+\dfrac4{x+3}$ (ii) $\ln\left(\dfrac{625}{216}\right)$

Three-factor logarithmic integral

Three-factor logarithmic integral

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