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Integrate the function $\frac{5x^3-4x}{x^4-16}$ from $3$ 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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Rewrite the expression $\frac{5x^3-4x}{x^4-16}$ inside the integral in factored form

$\int_{3}^{4}\frac{5x^3-4x}{-\left(4+x^2\right)\left(2+x\right)\left(2-x\right)}dx$

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

$\int_{3}^{4}\frac{5x^3-4x}{-\left(4+x^2\right)\left(2+x\right)\left(2-x\right)}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function (5x^3-4x)/(x^4-16) from 3 to 4. Rewrite the expression \frac{5x^3-4x}{x^4-16} inside the integral in factored form. Take the constant \frac{1}{-1} out of the integral. Rewrite the fraction \frac{5x^3-4x}{\left(4+x^2\right)\left(2+x\right)\left(2-x\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(4+x^2\right)\left(2+x\right)\left(2-x\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 ((5x^3+-4x)/(x^4-16))dx from 3 to 4 using partial fractionsSolve integral of ((5x^3+-4x)/(x^4-16))dx from 3 to 4 using basic integralsSolve integral of ((5x^3+-4x)/(x^4-16))dx from 3 to 4 using u-substitutionSolve integral of ((5x^3+-4x)/(x^4-16))dx from 3 to 4 using integration by partsSolve integral of ((5x^3+-4x)/(x^4-16))dx from 3 to 4 using trigonometric substitution

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Function Plot

Plotting: $\frac{5x^3-4x}{x^4-16}$

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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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