How do you find the integral of $int (cos(1/t))/(t^2)dt$ ?

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Answer 1 · 2018-04-26T00:45:33

$int \ (cos(1/t))/t^2 \ dt = -sin(1/t) + C$

We seek:

$I = int \ \ (cos(1/t))/t^2 \ dt$

We can perform a substitution, Let:

$u=1/t => (du)/dt = -1/t^2$

Then we can transform the integral:

$I = int \ \ (cos(u))/(-1) \ du$
$\ \ = -sin u + C$

Then, restoring the substitution, we get:

$I = -sin(1/t) + C$

How do you find the integral of int (cos(1/t))/(t^2)dtint (cos(1/t))/(t^2)dt?