Consider the integral $$\int \frac{x^{21}-5 x^{14}+5 x^7-10}{\left(x^3-4 x^2+3 x\right)^3 \left(x^4-81\right)^2} \,dx$$ Enter a T or an F in each answer space below to indicate whether or not a term of the given type occurs in the general form of the complete partial fractions decomposition of the integrand. $A_1, A_2, A_3\dots$ and $B_1, B_2, B_3,\dots$ denote constants.
You must get all of the answers correct to receive credit.

1. $\frac{B_1}{\left(x- 1\right)^3}$
2. $\frac{B_{3}}{\left(x- 3\right)^5}$
3. $A_{1} x$
4. $\frac{B_{2}}{\left(x- 3\right)^4}$
5. $A_{3} x^5$
6. $\frac{B_{4}}{\left(x - 1\right)^2}$
7. $A_{2} x^4$