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 $1$ Over x EndFraction plus StartFraction $1$ Over x squared plus $4$ x plus $5$ EndFraction right parenthesis dx$$StartFraction $1$ Over x EndFraction plus StartFraction $1$ Over x squared plus $4$ x plus $5$ EndFraction$1$x$+1$x$2+4$x$+5$dx$,$

which is more readily evaluated.

Your answer is correct.

B$.$

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

Part $2$

Evaluate the indefinite integral.

Integral from nothing to nothing StartFraction x squared plus $5$ x plus $5$ Over x left parenthesis x squared plus $4$ x plus $5$ right parenthesis EndFraction dx$$x$2+5$x$+5$xx$2+4$x$+5$dxequals$=$enter your response here