Evaluate the integral $\int \left( \sin ^ { 3 } ( 2 t ) \cos ( 2 t ) \right) \mathbf { i } + t ^ { 2 } \ln t \mathbf { j } + \frac { e ^ { \sqrt { t } } } { \sqrt { t } } \mathbf { k }$

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The Answer of Evaluate the integral $\int \left( \sin ^ { 3 } ( 2 t ) \cos ( 2 t ) \right) \mathbf { i } + t ^ { 2 } \ln t \mathbf { j } + \frac { e ^ { \sqrt { t } } } { \sqrt { t } } \mathbf { k }$

Evaluate the Integral