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Integrate the function $\frac{n+5}{n^2}$ from $1$ to $\infty $

Step-by-step Solution

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Solving: $\int_{1}^{\infty }\frac{n+5}{n^2}dn$
Solve instead: $\int_1^{\infty}\left(\frac{n+5}{n^2}\right)dx$

Solution

Formulas

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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 (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.

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Function Plot

Plotting: $\frac{n+5}{n^2}$

Similar Problems Solved

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{x^2}\right)dx$

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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 (3)

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