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

The integral from n to n+1 of 1/(1+x^2) is arctan(n+1)-arctan(n)

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

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

arctan (n + 1) - arctan (n)

Solution steps

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

Use the common integral:

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

= [arctan (x)]_{n}^{n + 1}

Compute the boundaries:

arctan (n + 1) - arctan (n)

= arctan (n + 1) - arctan (n)

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What is the integral from n to n+1 of 1/(1+x^2) ?
The integral from n to n+1 of 1/(1+x^2) is arctan(n+1)-arctan(n)