Calculate the indefinite integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}[(2t+2)i+(2t+2{)}^{2}j+(2t+2{)}^{-1}k]dt$

Select the correct vector.

$\frac{(2t+2{)}^2}{4}i+\frac{(2t+2{)}^3}{6}j-\frac{1}{4(2t+2{)}^2}k+c$

$2i+6(2t+2{)}^{2}j-\frac{2}{(2t+2{)}^2}k+c$

$\frac{(2t+2{)}^2}{2}i+\frac{(2t+2{)}^3}{3}j+ln|2t+2|k+c$

$\frac{(2t+2{)}^2}{4}i+\frac{(2t+2{)}^3}{6}j+\frac{ln|2t+2|}{2}k+c$