Question

What is `int (ln(3x-1))^-2dx`?

Answer 1

There's no known results of this equation.

Explanation:

`int1/(ln(3x-1)²)dx`

Let `X=3x-1`

`dX=3dx`
So:
`int1/(ln(3x-1)²)dx=1/3int1/(ln(X)²)dX`
Now let `Y=ln(X)`
`X=e^Y`
`dX=e^YdY`
So:

`1/3int1/(ln(X)²)dX=1/3inte^Y/(Y²)dY`
Using integration by parts :
`intf*g'dY=f*g-intg*f'dY`
There:
`f(Y)=e^Y`, `g'(Y)=1/(Y²)`
`f'(Y)=e^Y`, `g(Y)=-1/Y`

`1/3inte^Y/(Y²)dY=1/3(-e^Y/Y)+1/3inte^Y/YdY`

But because of Liouville's theorem, there's no known solutions for `inte^Y/YdY`
\0/ here's our answer !