Compute the indefinite integral $of$ the following function.

$r(t)=t{e}^{t}i+t^{3}cos{t}^{4}j+\frac{5t^4}{\sqrt[\phantom{2}]{t^5+3}}k$

Select the correct choice below and fill $in$ the answer boxes $to$ complete your choice.

$A.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}r(t)dt=1,|i+|,|j+|,|k+C$

$B.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}r(t)dt=1,|i+|,|j+,k$