# The Integral of Sin ln x by Parts

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 $u = \ln x \Rightarrow x = {e^x}$, then by differentiation $dx = {e^u}du$, we have

Here the first function is ${e^u}$ and the second function is $\sin u$

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 $I = \int {{e^u}\sin u} du$, we have