Evaluate the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(3t^2\sqrt[\phantom{2}]{t^3{t}^{2}1}2t\sqrt[\phantom{2}]{t^3{t}^{2}1})dt$

Select one:

a$.-\frac{2}{3}(t^3{t}^{2}1{)}^{\frac{3}{2}}C$

b$.\frac{2}{3}(t^3{t}^{2}1{)}^{\frac{3}{2}}C$

c$.\frac{2}{3}{t}^{\frac{9}{2}}\frac{2}{3}{t}^{\frac{6}{2}}1C$

d$.$ None of the above