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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

Problem to solve:

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Specify the solving method

1

Rewrite the expression $\frac{1}{x^2-6x+5}$ inside the integral in factored form

$\int_{2}^{4}\frac{1}{\left(x-1\right)\left(x-5\right)}dx$
2

Rewrite the fraction $\frac{1}{\left(x-1\right)\left(x-5\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{\left(x-1\right)\left(x-5\right)}=\frac{A}{x-1}+\frac{B}{x-5}$

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

$\int_{2}^{4}\frac{1}{\left(x-1\right)\left(x-5\right)}dx$

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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. Rewrite the expression \frac{1}{x^2-6x+5} inside the integral in factored form. 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). Multiplying polynomials.

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 int(1/(x^2-6x+5))dx&2&4 using partial fractionsSolve int(1/(x^2-6x+5))dx&2&4 using basic integralsSolve int(1/(x^2-6x+5))dx&2&4 using u-substitutionSolve int(1/(x^2-6x+5))dx&2&4 using integration by partsSolve int(1/(x^2-6x+5))dx&2&4 using trigonometric substitution

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$\int_{-5}^{5}\frac{1}{\sqrt{5-x}}dx$

Evaluate the integral

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

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$\int_{2}^{4}\left(x^2+5x+6\right)dx$

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$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Evaluate the integral

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$
$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.12 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegrals by Partial Fraction ExpansionMatricesGaussian Elimination

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