Express $\frac{5x^2+3x+7}{(x+1)(x-2)^2}$ in partial fractions.[6] Hence find \(\int \frac{5x^2+3x+

Question

Express $\frac{5x^2+3x+7}{(x+1)(x-2)^2}$ in partial fractions.[6] Hence find $\int \frac{5x^2+3x+7}{(x+1)(x-2)^2}\, dx$.[3]

Accepted Answer

(a) $\frac{1}{x+1}+\frac{4}{x-2}+\frac{11}{(x-2)^2}$ (b) $\ln|x+1|+4\ln|x-2|-\frac{11}{x-2}+C$

2025 JVSS PRELIMS P1 Q7