My Calculus 2 professor wants us to be able to set up partial fraction templates for complicated integrals. I don't know of a way to check my work without meeting with him, and he is unavailable right now, so I'm asking here.
$$\int \frac{3}{(x^2-6x+5)^2(x^2+x+2)^2}dx$$
$$=\int \frac{3}{[(x-1)(x-5)]^2(x^2+x+2)^2}dx$$
$$=\int \frac{A}{x-1}+\frac{B}{x-5}+\frac{C}{x-1}+\frac{D}{x-5} +\frac{Ex+\Delta}{x^2+x+2}+\frac{Fx+\theta}{x^2+x+2}dx$$
Is this the correct way to set up the integral to be integrated using the partial fractions method? If not, what did I do wrong?
The $C,$ $D,$ and $Fx+\theta$ terms should have the denominator squared. I would use Roman letters instead of the Greek in the last two terms.