What is the integral from 0 to infinity of 1/(1+x^2) ?

The integral from 0 to infinity of 1/(1+x^2) is pi/2

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integral from 0 to infinity of 1/(1+x^2)

\int_{0}^{\infty} \frac{1}{1 + x ^{2}} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{\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_{0}^{\infty} \frac{1}{1 + x ^{2}} d x = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

9 cos (π x), 12 x^{2} - 3, - 0.5, 0.5

x \to 0 lim (\frac{4 x}{tan ( x )})

\int [\frac{100}{25 + ( 5 y ) ^{2}} + e^{4}] d y

y^{^{'}} = e^{2 x} + 3 y

\int \frac{1}{x ^{2} + a ^{2}} d x

What is the integral from 0 to infinity of 1/(1+x^2) ?
The integral from 0 to infinity of 1/(1+x^2) is pi/2