Integrate the function $\frac{x-4}{x^2-5x+6}$ from $9$ to $1$

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$\int_{9}^{1}\frac{x-4}{\left(x-2\right)\left(x-3\right)}dx$

Learn how to solve problems step by step online. Integrate the function (x-4)/(x^2-5x+6) from 9 to 1. Rewrite the expression \frac{x-4}{x^2-5x+6} inside the integral in factored form. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Rewrite the fraction \frac{x-4}{\left(x-2\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x-2\right)\left(x-3\right).