# Integration of lnx Squared

In this tutorial we shall find the integral of ${\left( {\ln x} \right)^2}$ function, and it is another important integration. To evaluate this integral first we use the method of substitution and then we use integration by parts.

The integral of $\ln x$ squared is of the form

But $z = \ln x$ implies that ${e^z} = x$, by differentiation ${e^z}dz = dx$, so the given integral (i) takes the form

Considering ${z^2}$ and ${e^z}$ are the first and second functions and using integration by parts, we have

Using the formula for integration by parts, we have

Using the formula above, equation (ii) becomes

Now again using integration by parts, we have

From the above substitution it can be written in the form