What is $\int \frac{cos (\frac{1}{t})}{t^{2}} d t$ $int (cos(1/t))/(t^2)dt$ ?

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Answer 1 · 2016-02-13T11:51:55

$- sin (\frac{1}{t}) + C$ $-sin(1/t) + C$

We can use a substitution. I would recommend using:
$u = \frac{1}{t}$ $u =1/t$

From this we get:
$d u = - \frac{1}{t^{2}} d u$ $du = -1/t^2du$

If we now put this into the integral then it will reduce tot:

$\int - cos (u) d u$ $int-cos(u) du$

Which will integrate to give us:

$- sin (u) + C$ $-sin(u) +C$

Now reverse the substitution:

$- sin (\frac{1}{t}) + C$ $-sin(1/t) + C$

What is ∫cos(1t)t2dtint (cos(1/t))/(t^2)dt ?