In the Three Previous Problems, the Solution for the Temperature $u ( x , t )$

In the three previous problems, the solution for the temperature $u ( x , t )$ is

A) $u = u _ { 0 } \int _ { 0 } ^ { \infty } \left[ \sin ( \alpha x ) \left( 1 - e ^ { - k \alpha ^ { 2 } t } \right) / \alpha \right] d \alpha$
B) $u = u _ { 0 } \int _ { 0 } ^ { \infty } \left[ \sin ( \alpha x ) \left( 1 - e ^ { - k \alpha ^ { 2 } t } \right) / \alpha \right] d \alpha / \pi$
C) $u = 2 u _ { 0 } \int _ { 0 } ^ { \infty } \left[ \sin ( \alpha x ) \left( 1 - e ^ { k \alpha ^ { 2 } t } \right) / \alpha \right] d \alpha$
D) $u = 2 u _ { 0 } \int _ { 0 } ^ { \infty } \left[ \sin ( \alpha x ) \left( 1 - e ^ { k \alpha ^ { 2 } t } \right) / \alpha \right] d \alpha / \pi$
E) $u = 2 u _ { 0 } \int _ { 0 } ^ { \infty } \left[ \sin ( \alpha x ) \left( 1 - e ^ { - k \alpha ^ { 2 } t } \right) / \alpha \right] d \alpha / \pi$