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

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

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

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

π

Decimal Notation

3.14159 \dots

Solution steps

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

Compute the indefinite integral:

\int \frac{4}{1 + x ^{2}} d x = 4 arctan (x) + C

Compute the boundaries:

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

= 2 π - π

Simplify

= π

\int \frac{1}{2 cos ( x )} d x

\frac{110}{x ^{12}}

x^{^{''}} = - 9 x

\frac{d}{d x} ((\frac{2 x ^{2} - x ^{- 2}}{4 x + 3})^{\frac{3}{4}})

\frac{1}{x}, 4

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