pi -- 2 e / | | sin(log(x)) | ----------- dx | x | / 1
Integral(sin(log(x))/x, (x, 1, exp(pi/2)))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of sine is negative cosine:
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 sine is negative cosine:
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | | sin(log(x)) | ----------- dx = C - cos(log(x)) | x | /
Use the examples entering the upper and lower limits of integration.