What is int (ln(3x-1))^-2dx(ln(3x1))2dx?

1 Answer
May 21, 2018

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 !