Integration by Partial Fraction
📥 Download Partial Fractions PDF Integration by Partial Fractions — Examples & Solutions Integration by Partial Fractions Types and worked examples (converted from the uploaded notes). Type 1: Distinct linear factors When the denominator is expressible as a product of distinct linear factors. Example 1 Evaluate \( \displaystyle \int \frac{x-1}{(x+1)(x-2)} \, dx \). Write \( \dfrac{x-1}{(x+1)(x-2)} = \dfrac{A}{x+1} + \dfrac{B}{x-2} \) Then \( x-1 = A(x-2) + B(x+1) \) Putting \(x=2\): \(1 = 3B \Rightarrow B=\tfrac{1}{3}\). Putting \(x=-1\): \(-2 = -3A \Rightarrow A=\tfrac{2}{3}\). Thus \( \dfrac{x-1}{(x+1)(x-2)} = \dfrac{2/3}{x+1} + \dfrac{1/3}{x-2} \) Integrate: \( \int \frac{x-1}{(x+1)(x-2)} dx = \frac{2}{3}\ln|x+1| + \frac{1}{3}\ln|x-2| + C \) Example 2 Evaluate \( ...