Find the integral.

$\(\int\)_{}^{}se^{3s}ds$

Find the indefinite integral.

$\(\int\)_{}^{}r^2e^{-r}dr$

Evaluate the indefinite integral.

$\(\int\)_{}^{}\(\left\)(s^2+4\(\right\))e^{3s}ds$

Evaluate the indefinite integral.

$\(\int\)^{}\(\frac{\ln x}{x^4}\)dx$

Evaluate the definite integral.

$\(\int\)_1^2x\(\ln\) xdx$

The rate of growth of a particular bacteria is given by $b^{\prime }\left(t\right)=4t^2{e}^{.5t}$ where $t$ is time in days. What is the total growth of the population of bacteria during the first 5 days?