Final answer to the problem
The integral diverges.
Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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1
Expand the fraction $\frac{n+5}{n^2}$ into $2$ simpler fractions with common denominator $n^2$
$\int\left(\frac{n}{n^2}+\frac{5}{n^2}\right)dn$
Learn how to solve differential calculus problems step by step online.
$\int\left(\frac{n}{n^2}+\frac{5}{n^2}\right)dn$
Learn how to solve differential calculus problems step by step online. Integrate the function (n+5)/(n^2) from 1 to infinity. Expand the fraction \frac{n+5}{n^2} into 2 simpler fractions with common denominator n^2. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{n}+\frac{5}{n^2}\right)dn into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{n}dn results in: \ln\left(n\right).
Final answer to the problem
The integral diverges.
