Evaluate the integral.

$9$r$2$r $+4$

$$dr

Step $1$

We will use long division to re$-$write the integrand of

$9$r$2$r $+4$

$$dr

$.$

We must calculate

r $+49$r$2+0$r $+0.$

After the first step of long division, we get

$$

$$$9$r

r $+49$r$2+0$r$+0(9$r$2+36$r$)$

$$$36$r$+0$

$.$

Step $2$

After the next step, we get

$9$r $$

$$$36$

r $+49$r$2+0$r$+0(9$r$2+36$r$)$

$36$r$+0(36$r$144)$

$$$144$

$.$

Step $3$

As a result, we have

$9$r$2$r $+4$

$$dr

$=$

$9$

$9$

r $36+$

$144$r $+4$

$4$

$$dr

$.$

Step $4$

Ignoring the constant of integration, we have

$$

$(9$r $36)$ dr

$=$

$9$r$2218$r$+144$ln$|$r$+4|$

$+$ C$.$