# Find # int \ ln(lnx)/x \ dx#?

##### 2 Answers

Dec 4, 2017

Substitution Method.

#### Explanation:

Let

Now differentiate this on both sides.

Now,

Write

Dec 4, 2017

# int \ ln(lnx)/x \ dx = lnxln(lnx)-lnx + c #

#### Explanation:

Assuming logarithm base

# I = int \ ln(lnx)/x \ dx #

We can perform a substitution:

# u= lnx => (du)/dx=1/x #

Substituting into the integral we get:

# I = int \ lnu \ du #

This is now a standard integral (and can be readily derived with an application of Integration By Parts), and we have:

# I = u lnu-u + c #

And restoring the substitution we have:

# I = lnxln(lnx)-lnx + c #