9 / | | cos(log(x)) | ----------- dx | x | / 1
Integral(cos(log(x))/x, (x, 1, 9))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of cosine is sine:
Now substitute back in:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | | cos(log(x)) | ----------- dx = C + sin(log(x)) | x | /
sin(log(9))
=
sin(log(9))
sin(log(9))
Use the examples entering the upper and lower limits of integration.