In this tutorial we shall derive the integral of sin(lnx) and solve this problem with the help of the integration by parts methods as well as with the help of the substitution method.
The integral of sin(lnx) is of the form
Suppose that , then by differentiation , we have
Here the first function is and the second function is
Using the formula for integration by parts, we have
Using the formula above, equation (i) becomes
Again using integration by parts, we have
Using the original integral form as , we have