Hi, I have the problem:
and it states that the integrand has partial fractions decomposition:
So then I need to make
Now, would ax^3=7? I know what to do with simple A and B partial fractions but this is looking difficult especially when there is multiple variables multiplied by each other. How can I solve this?
We have: .
Note that I immediately made two fractions for the quadratic.
I discovered this trick a half-century ago and have taught it that way ever since.
It seems that no teacher has discovered this yet!
Multiply through by the LCD:
Add  and : .
Solve this system: .
. . which can be readily integrated . . .
Well, my teacher taught it to us... and I'm sure he's not the only one. Some people used it on MHF tooIt seems that no teacher has discovered this yet!
And this teacher went further than this by taking the derivative when we had something like x and x² in the partial fractions decomposition. ^^'