# Integral of Sin ln x by Parts

In this tutorial we shall drive integral of sin(lnx), and solve this problem with the help of integration by parts methods as well as with the help of 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 first function is ${e^u}$ and second function will be $\sin u$
Using formula for integration by parts, we have

Equation (i) becomes using above formula, we have

Again using integration by parts, we have

Using the original integral form as $I = \int {{e^u}\sin u} du$, we have