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

Step-by-step Solution

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Solution

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Final Answer

The integral diverges.

Step-by-step Solution

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We could not solve this problem by using the method: Integrate by parts

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Factor the trinomial $x^2-6x+5$ finding two numbers that multiply to form $5$ and added form $-6$

$\begin{matrix}\left(-1\right)\left(-5\right)=5\\ \left(-1\right)+\left(-5\right)=-6\end{matrix}$

Learn how to solve definite integrals problems step by step online.

$\begin{matrix}\left(-1\right)\left(-5\right)=5\\ \left(-1\right)+\left(-5\right)=-6\end{matrix}$

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Learn how to solve definite integrals problems step by step online. Integrate the function 1/(x^2-6x+5) from 2 to 4. Factor the trinomial x^2-6x+5 finding two numbers that multiply to form 5 and added form -6. Thus. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x-5\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-1\right)\left(x-5\right).

Final Answer

The integral diverges.

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (1/(x^2+-6x))dx from 2 to 4 using partial fractionsSolve integral of (1/(x^2+-6x))dx from 2 to 4 using basic integralsSolve integral of (1/(x^2+-6x))dx from 2 to 4 using u-substitutionSolve integral of (1/(x^2+-6x))dx from 2 to 4 using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{x^2-6x+5}$

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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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