Final answer to the problem
The integral diverges.
Step-by-step Solution
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1
Expand the fraction $\frac{\left(5x\right)^3-9\left(5x\right)^2+135x-27}{x^3}$ into $4$ simpler fractions with common denominator $x^3$
$\int\left(\frac{\left(5x\right)^3}{x^3}+\frac{-9\left(5x\right)^2}{x^3}+\frac{135x}{x^3}+\frac{-27}{x^3}\right)dx$
Learn how to solve powers of powers problems step by step online.
$\int\left(\frac{\left(5x\right)^3}{x^3}+\frac{-9\left(5x\right)^2}{x^3}+\frac{135x}{x^3}+\frac{-27}{x^3}\right)dx$
Learn how to solve powers of powers 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.
