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Integrate the function $\frac{x^3-4x-10}{x^2-x-6}$ from 0 to $1$

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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Rewrite the expression $\frac{x^3-4x-10}{x^2-x-6}$ inside the integral in factored form

$\int_{0}^{1}\frac{x^3-4x-10}{\left(x+2\right)\left(x-3\right)}dx$

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

$\int_{0}^{1}\frac{x^3-4x-10}{\left(x+2\right)\left(x-3\right)}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function (x^3-4x+-10)/(x^2-x+-6) from 0 to 1. Rewrite the expression \frac{x^3-4x-10}{x^2-x-6} inside the integral in factored form. Expand. Divide x^3-4x-10 by x^2-x-6. Resulting polynomial.

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 ((x^3+-4x)/(x^2+-1x))dx from 0 to 1 using partial fractionsSolve integral of ((x^3+-4x)/(x^2+-1x))dx from 0 to 1 using basic integralsSolve integral of ((x^3+-4x)/(x^2+-1x))dx from 0 to 1 using u-substitutionSolve integral of ((x^3+-4x)/(x^2+-1x))dx from 0 to 1 using integration by partsSolve integral of ((x^3+-4x)/(x^2+-1x))dx from 0 to 1 using trigonometric substitution

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Function Plot

Plotting: $\frac{x^3-4x-10}{x^2-x-6}$

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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

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