Define the rational function

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Define the rational function f(x)=2x+3(x−1)(x+2)f(x)=\dfrac{2x+3}{(x-1)(x+2)}.\ Let L=∫24f(x) dxL=\displaystyle \int_{2}^{4} f(x)\,dx. (1) Part 1: Find an antiderivative F(x)F(x) of f(x)f(x). (2) Part 2: Use F(x)F(x) to determine the exact value of LL.

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