`int cos(pi/x)/(x^2) dx` Evaluate the indefinite integral.

Expert Answers

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Given `intcos(pi/x)/x^2dx`

integrate using the Substitution Rule.

Let `u=pi/x`

or `u=pix^-1`

`(du)/dx=-pix^-2`

`(du)/dx=-pi/x^2`

`dx=x^2/-pi*du`

 

`=intcos(u)/x^2*(x^2/-pi)du`

`=1/-piintcos(u)du`

`=1/-pisin(u)+C`

`=1/-pisin(pi/x)+C`

 

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