What is the integral from 1 to infinity of (1/x)^2 ?

The integral from 1 to infinity of (1/x)^2 is 1

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integral from 1 to infinity of (1/x)^2

\int_{1}^{\infty} (\frac{1}{x})^{2} d x

1

Solution steps

\int_{1}^{\infty} (\frac{1}{x})^{2} d x

Compute the indefinite integral:

\int (\frac{1}{x})^{2} d x = - \frac{1}{x} + C

Compute the boundaries:

\int_{1}^{\infty} (\frac{1}{x})^{2} d x = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

What is the integral from 1 to infinity of (1/x)^2 ?
The integral from 1 to infinity of (1/x)^2 is 1