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

The integral from 1 to infinity of 1/(1+x^2) is pi/4

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

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

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{1 + x ^{2}} d x = \frac{π}{2} - \frac{π}{4}

= \frac{π}{2} - \frac{π}{4}

Simplify

= \frac{π}{4}

\frac{d}{d x} (x - 2 - 0.5 sin (x))

\frac{d}{d s} (s t)

f (x) = - 4 sin (x)

2 x + 5

x y^{^{'}} + (ln (x)) y = 0

What is the integral from 1 to infinity of 1/(1+x^2) ?
The integral from 1 to infinity of 1/(1+x^2) is pi/4