Why Is the Integral of 1/(4-ln(x)) Challenging?

[KillaKem]

Homework Statement

Find the integral, I , of the followin' function.

Homework Equations

$$\int \frac{dx}{4 - lnx}$$.

3.Attempt

U = sqrt(lnx)
dx = 2xlnx du

Therefore

$$\int \frac{2xlnxdu}{4 - U^2}$$.

Integration of this f(x) failed

These are all integrals we have dealt with

http://www.mathwords.com/i/integral_table.htm

 

[gabbagabbahey]

Find the integral, I , of the followin' function.

Homework Equations

$$\int \frac{dx}{4 - lnx}$$.

There is no closed-form solution in terms of elementary functions, but if you use the substitution $u=4-\ln(x)$, you can express the integral in terms of the special function called exponential integral function.