Evaluate the integral of ((cos(1/x))/x^2)?

Answer 1

Let u = 1/x
du = -1/x^2 * dx

So integral transforms to
-cos(u) * du
which integrates to
-sin(u) = -sin(1/x) + constant

Answer 2

if you put 1/x=z (-1/x^2)*dx = dz
and the integral becomes
-Int cos z dz = -sin z +C = -sin (1/x) +C

Answer 3

substitute (1/x) = t (some dummy variable t)
then dx/x^2 will be replaced by -dt
integrate cos(t)(- dt)
answer is - sin(t) + constant

final answer: - sin (1/x) + constant

Answer 4

Simply let u = 1/x.
integral of -cosu du

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