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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\r
( 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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