The Solution $\mathbf { r } ( t )$ To the Differential Equation

Multiple Choice

The solution $\mathbf { r } ( t )$ to the differential equation $\mathbf { r } ^ { \prime } ( t ) = 3 t ^ { 2 } \mathbf { i } - \frac { 1 } { t - 3 } \mathbf { j } + 4 \mathbf { k }$ with the condition $\mathbf { r } ( 4 ) = \mathbf { i } - \mathbf { j } + 3 \mathbf { k }$ is

A) $- \left( t ^ { 3 } - 63 \right) \mathbf { i } - ( \ln | t - 3 | + 1 ) \mathbf { j } + ( 4 t - 13 ) \mathbf { k }$
B) $\left( t ^ { 3 } - 63 \right) \mathbf { i } + ( \ln | t - 3 | + 1 ) \mathbf { j } - ( 4 t - 13 ) \mathbf { k }$
C) $\left( t ^ { 3 } - 63 \right) \mathbf { i } - ( \ln | t - 3 | + 1 ) \mathbf { j } - ( 4 t - 13 ) \mathbf { k }$
D) $\left( t ^ { 3 } - 63 \right) \mathbf { i } - ( \ln | t - 3 | + 1 ) \mathbf { j } + ( 4 t - 13 ) \mathbf { k }$
E) $\left( t ^ { 3 } - 63 \right) \mathbf { i } + ( \ln | t - 3 | + 1 ) \mathbf { j } + ( 4 t - 13 ) \mathbf { k }$