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

The integral from 1 to infinity of 1/(n^2+1) is diverges

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integral from 1 to infinity of 1/(n^2+1)

\int_{1}^{\infty} \frac{1}{n ^{2} + 1}

diverges

Solution steps

\int_{1}^{\infty} \frac{1}{n ^{2} + 1} d x

Compute the indefinite integral:

\int \frac{1}{n ^{2} + 1} d x = \frac{x}{n ^{2} + 1} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{n ^{2} + 1} d x =

diverges

= diverges

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