Consider the following integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{t}{1-t^8}dt,$ where $t1.$

A$.$ Technically, the integrand is a rational polynomial. This should indicate that we are to try$/$use the Partial Fraction Decomposition $($PFD$)$ integration technique. Upon considering the integrand, why would the PFD technique not work well for this integral?

B$.$ Using whiat you know about geometric series, please rewrite the above integrand as a power series.

C$.$ Using the power series that you found in part $($B$),$ please calculate: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{t}{1-t^8}dt$