Need help finding this Antiderivative

Question

I have no idea how to do that, help please

I was trying a change of variables in integration but nothing $$ \int \frac{x3^{x-a}}{3^{3x-a} + 3^{2x+1} + 3^{x+a+1} + 3^{2a}}\, dx $$

Answer 1

Hint:

You can multiply by

$$ \frac{3^a}{3^a} $$

Then you get

$$ 3^{3x} + 3^1 3^{2x} 3^a + 3^1 3^x a^{2a} + 3^{3a} = \Big( 3^x + 3^a \Big)^3 $$

as the denominator...

So you get

$$ \int \frac{x 3^x}{\Big( 3^x + 3^a \Big)^3} dx $$