Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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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: $\int_a^bf(x)dx=-\int_b^af(x)dx$
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$-\int_{1}^{8}\frac{x-4}{x^2-5x+6}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (x-4)/(x^2-5x+6) from 8 to 1. 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. Factor the trinomial x^2-5x+6 finding two numbers that multiply to form 6 and added form -5. Thus. Rewrite the fraction \frac{x-4}{\left(x-2\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition.