Evaluate the integral \int\frac{\cos(1-\ln(y))}{y}dy

Step 1
We have to find the integrals:
${\displaystyle \int \frac{\cos (1-\ln \left(y\right))}{y}dy}$
We will find this integrals by substitution method
Let ${\displaystyle t=1-\ln \left(y\right)}$
Differentiating both sides with respect to 'y', we get
${\displaystyle t=1-\ln \left(y\right)}$
${\displaystyle dt=0-\frac{1}{y}dy}$
${\displaystyle -dt=\frac{dy}{y}}$
Step 2
Now finding integrals putting above value,
$\int \frac{\cos (1-\ln (y))}{y}dy=\int \cos (1-\ln (y))\frac{dy}{y}$
${\displaystyle =\int \cos tdt}$
${\displaystyle =\sin t+c}$
Since integration of cosine function is sine.
Now putting ${\displaystyle t=1-\ln \left(y\right)}$, we get
${\displaystyle =\sin (1-\ln \left(y\right))+c}$.
Hence, integrals of the given expression is ${\displaystyle \sin (1-\ln \left(y\right))+c}$.