Find the general antiderivative of : `f(x)= (cos(pi/x))/(x^2)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The anti-derivative `int (cos(pi/x))/(x^2) dx` has to be determined.

Let `pi/x = u`

`du = -pi/x^2 dx`

`int (cos(pi/x))/(x^2) dx`

=> `-(1/pi)*int cos u du`

=> `-(1/pi)*sin u `

=> `-(1/pi)*sin(pi/x) + C`

The anti-derivative `int (cos(pi/x))/(x^2) dx = -(1/pi)*sin(pi/x) + C`

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