1 / | | cos(log(x)) | ----------- dx | 2 | x | / 0
Integral(cos(log(x))/x^2, (x, 0, 1))
Let .
Then let and substitute :
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Use integration by parts, noting that the integrand eventually repeats itself.
For the integrand :
Let and let .
Then .
For the integrand :
Let and let .
Then .
Notice that the integrand has repeated itself, so move it to one side:
Therefore,
So, the result is:
Now substitute back in:
Use integration by parts, noting that the integrand eventually repeats itself.
For the integrand :
Let and let .
Then .
For the integrand :
Let and let .
Then .
Notice that the integrand has repeated itself, so move it to one side:
Therefore,
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | cos(log(x)) sin(log(x)) cos(log(x)) | ----------- dx = C + ----------- - ----------- | 2 2*x 2*x | x | /
<-oo, oo>
=
<-oo, oo>
AccumBounds(-oo, oo)
Use the examples entering the upper and lower limits of integration.