What is the integral from n to infinity of 1/(x^5) ?

The integral from n to infinity of 1/(x^5) is 1/(4n^4)

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integral from n to infinity of 1/(x^5)

\int_{n}^{\infty} \frac{1}{x ^{5}} d x

\frac{1}{4 n ^{4}}

Solution steps

\int_{n}^{\infty} \frac{1}{x ^{5}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}} + C

Compute the boundaries:

\int_{n}^{\infty} \frac{1}{x ^{5}} d x = 0 - (- \frac{1}{4 n ^{4}})

= 0 - (- \frac{1}{4 n ^{4}})

Simplify

= \frac{1}{4 n ^{4}}

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What is the integral from n to infinity of 1/(x^5) ?
The integral from n to infinity of 1/(x^5) is 1/(4n^4)