Question

Express the function 𝑓(𝑥) = 𝑥 (𝑥−3)2 as partial fractions and hence find ∫ 𝑓(𝑥)𝑑�

Answer 1

$f(x)=\frac{x}{(x-3)^2}$

$\frac{x}{(x-3)^2}=\frac{x-3+3}{(x-3)^2}=\frac{1}{x-3}+\frac{3}{(x-3)^2}$

$\int(\frac{1}{x-3}+\frac{3}{(x-3)^2})dx=log(x-3)-\frac{3}{x-3}+C$