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

Reeves 2020-11-08 Answered
Evaluate the integral cos(1ln(y))ydy
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Expert Answer

ottcomn
Answered 2020-11-09 Author has 97 answers

Step 1
We have to find the integrals:
cos(1ln(y))ydy
We will find this integrals by substitution method
Let t=1ln(y)
Differentiating both sides with respect to 'y', we get
t=1ln(y)
dt=01ydy
dt=dyy
Step 2
Now finding integrals putting above value,
cos(1ln(y))ydy=cos(1ln(y))dyy
=costdt
=sint+c
Since integration of cosine function is sine.
Now putting t=1ln(y), we get
=sin(1ln(y))+c.
Hence, integrals of the given expression is sin(1ln(y))+c.

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