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f(x)=(x^2-4x+3)/(x^2-2x+1)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫x2−4x+3x2−2x+1dx\int\frac{x^2-4x+3}{x^2-2x+1}dx

Step-by-step Solution

Learn how to solve problems step by step online. Find the integral int((x^2-4x+3)/(x^2-2x+1))dx. Rewrite the expression \frac{x^2-4x+3}{x^2-2x+1} inside the integral in factored form. Factor the trinomial x^2-4x+3 finding two numbers that multiply to form 3 and added form -4. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying.
Find the integral int((x^2-4x+3)/(x^2-2x+1))dx

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Final answer to the exercise

−2ln⁡∣x−1∣+x+C1-2\ln\left|x-1\right|+x+C_1

Try other ways to solve this exercise

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  • Integrate by partial fractions
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  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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∫x2−4x+3x2−2x+1 dx
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