What is the integral from 1 to infinity of 1/(x^{1.001)} ?

The integral from 1 to infinity of 1/(x^{1.001)} is 1000

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integral from 1 to infinity of 1/(x^{1.001)}

\int_{1}^{\infty} \frac{1}{x ^{1.001}} d x

1000

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{1.001}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{1.001}} d x = - \frac{1000}{x ^{0.001}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{1.001}} d x = 0 - (- 1000)

= 0 - (- 1000)

Simplify

= 1000

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What is the integral from 1 to infinity of 1/(x^{1.001)} ?
The integral from 1 to infinity of 1/(x^{1.001)} is 1000