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Integrate the function $\frac{\left(5x-3\right)^3}{x^3}$ from $1$ to $\infty $

Step-by-step Solution

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Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

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Learn how to solve improper integrals problems step by step online. Integrate the function ((5x-3)^3)/(x^3) from 1 to infinity. Expand the fraction \frac{\left(5x\right)^3-9\left(5x\right)^2+135x-27}{x^3} into 4 simpler fractions with common denominator x^3. Simplify the resulting fractions. Simplify the expression. The integral \int\frac{\left(5x\right)^3}{x^3}dx results in: 125x.

Final answer to the problem

The integral diverges.

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Function Plot

Plotting: $\frac{\left(5x-3\right)^3}{x^3}$

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Main Topic: Improper Integrals

An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number that is not part of the function's domain, or infinity.

Used Formulas

See formulas (4)

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