What is the integral from 2 to infinity of (8cos(pi/x))/(x^2) ?

The integral from 2 to infinity of (8cos(pi/x))/(x^2) is 8/pi

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integral from 2 to infinity of (8cos(pi/x))/(x^2)

\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x

\frac{8}{π}

Decimal Notation

2.54647 \dots

Solution steps

\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x

Compute the indefinite integral:

\int \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x = - \frac{8}{π} sin (\frac{π}{x}) + C

Compute the boundaries:

\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x = 0 - (- \frac{8}{π})

= 0 - (- \frac{8}{π})

Simplify

= \frac{8}{π}

h \to + 0 lim (\frac{\frac{1}{a + h} - \frac{1}{a}}{h})

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

\int t^{- 3} d t

\int \frac{x ^{3}}{25 + x ^{2}} d x

f (x) = - 3 x^{2} + 12, at x = 3

What is the integral from 2 to infinity of (8cos(pi/x))/(x^2) ?
The integral from 2 to infinity of (8cos(pi/x))/(x^2) is 8/pi