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# (Solved): ( 1 point) Consider the integral $\int \frac{x^{21}-8 x^{14}+6 x^{7}-23}{\left(x^{3}-4 x^{2}+3 x\ ... ( 1 point) Consider the integral \[ \int \frac{x^{21}-8 x^{14}+6 x^{7}-23}{\left(x^{3}-4 x^{2}+3 x\right)^{3}\left(x^{4}-81\right)^{2}} d x$ Enter a $$\mathrm{T}$$ or an $$\mathrm{F}$$ 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. $$A_{1}, A_{2}, A_{3} \ldots$$ and $$B_{1}, B_{2}, B_{3}, \ldots$$ denote constants. You must get all of the answers correct to receive credit. 1. $$\frac{A_{3} x+B_{3}}{x^{2}+9}$$ 2. $$\frac{A_{7} x+B_{7}}{(x+3)^{2}}$$ 3. $$\frac{B_{5}}{x^{4}}$$ 4. $$A_{1} x^{2}$$ (a product, not a fraction!) 5. $$\frac{B_{4}}{(x-1)^{4}}$$ 6. $$\frac{A_{2} x+B_{2}}{\left(x^{4}+81\right)^{2}}$$ 7. $$\frac{\boldsymbol{B}_{6}}{x+3}$$ 8. $$\frac{B_{1}}{x-3}$$

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