Evaluate the following integral.

Integral from nothing to nothing StartFraction x squared plus $9$ x plus $10$ Over x left parenthesis x squared plus $2$ x plus $10$ right parenthesis EndFraction dx$$x$2+9$x$+10$xx$2+2$x$+10$dx

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Part $1$

Can partial fraction decomposition be used to evaluate the given$$ integral? Select the correct choice below$$ and, if$$ necessary, fill in the answer box to complete your choice.

A$.$

$$Yes$,$ partial fraction decomposition can be used. The given integral can be rewritten as

Integral from nothing to nothing left parenthesis StartFraction Upper A Over x EndFraction plus StartFraction Bx plus Upper C Over x squared plus $2$ x plus $10$ EndFraction right parenthesis dx$$StartFraction Upper A Over x EndFraction plus StartFraction Bx plus Upper C Over x squared plus $2$ x plus $10$ EndFractionAx$+$Bx$+$Cx$2+2$x$+10$dx$,$

which is more readily evaluated.

B$.$

$$No$,$ partial fraction decomposition cannot be used.