Final Answer
$\frac{582}{83}$
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Step-by-step Solution
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1
Expand the fraction $\frac{15+2x^3}{x^4}$ into $2$ simpler fractions with common denominator $x^4$
$\int_{1}^{3}\left(\frac{15}{x^4}+\frac{2x^3}{x^4}\right)dx$
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$\int_{1}^{3}\left(\frac{15}{x^4}+\frac{2x^3}{x^4}\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (15+2x^3)/(x^4) from 1 to 3. Expand the fraction \frac{15+2x^3}{x^4} into 2 simpler fractions with common denominator x^4. Simplify the resulting fractions. Expand the integral \int_{1}^{3}\left(\frac{15}{x^4}+\frac{2}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{1}^{3}\frac{15}{x^4}dx results in: \frac{130}{27}.
Final Answer
$\frac{582}{83}$