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Integrate the function $\frac{1}{x-1}$ from 0 to $3$

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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Since the integral $\int_{0}^{3}\frac{1}{x-1}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{0}^{1}\frac{1}{x-1}dx+\int_{1}^{3}\frac{1}{x-1}dx$

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

$\int_{0}^{1}\frac{1}{x-1}dx+\int_{1}^{3}\frac{1}{x-1}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function 1/(x-1) from 0 to 3. Since the integral \int_{0}^{3}\frac{1}{x-1}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{0}^{1}\frac{1}{x-1}dx results in: \lim_{c\to0}\left(- \infty \right). The integral \int_{1}^{3}\frac{1}{x-1}dx results in: \lim_{c\to1}\left(\ln\left(2\right)-\ln\left(c-1\right)\right). Gather the results of all integrals.

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-1))dx from 0 to 3 using partial fractionsSolve integral of (1/(x-1))dx from 0 to 3 using basic integralsSolve integral of (1/(x-1))dx from 0 to 3 using u-substitutionSolve integral of (1/(x-1))dx from 0 to 3 using integration by partsSolve integral of (1/(x-1))dx from 0 to 3 using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{x-1}$

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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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