我在做一个课题的时候需要计算如下的积分表达式：
Integrate[(Subscript[t, obs])^\[Gamma] -
1/2 (Abs[Subscript[t, i] - Subscript[t, j] - x + y ])^\[Gamma], {x,
Subscript[t, 1], Subscript[t, 2]}, {y, Subscript[t, 3], Subscript[t,
4]}, Assumptions ->
0 < Subscript[t, 1] < Subscript[t, 2] &&
0 < Subscript[t, 3] < Subscript[t, 4] &&
Subscript[t, 4] - Subscript[t, 3] <=
Subscript[t, 2] - Subscript[t, 1] && Subscript[t, obs] > 0 &&
Subscript[t, i] > 0 && Subscript[t, j] > 0 && \[Gamma] > 0 &&
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
3] < 0 <
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
4] < Subscript[t, i] - Subscript[t, j] - Subscript[t, 1] +
Subscript[t, 3] <
Subscript[t, i] - Subscript[t, j] + Subscript[t, 4] - Subscript[t,
1] && Subscript[t, low] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
3] && Subscript[t, mid1] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
4] &&
Subscript[t, mid2] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 1] + Subscript[t,
3] && Subscript[t, hig] ==
Subscript[t, i] - Subscript[t, j] + Subscript[t, 4] - Subscript[t,
1]]
截图如下：
但是似乎过于复杂，算了很久也算不出结果。我曾经计算过同样的积分在0<tlow<tmid1<tmid2<thig情况下的积分，花的时间也很长，能够算出结果，但得到的是分成多种情况的条件表达式（实际上应该有一个统一的表达式）。请问各位，应当如何设置积分和Simplify时的Assumptions，使得积分能算出结果，并且最终的表达式尽可能简单呢？多谢！
Integrate[(Subscript[t, obs])^\[Gamma] -
1/2 (Abs[Subscript[t, i] - Subscript[t, j] - x + y ])^\[Gamma], {x,
Subscript[t, 1], Subscript[t, 2]}, {y, Subscript[t, 3], Subscript[t,
4]}, Assumptions ->
0 < Subscript[t, 1] < Subscript[t, 2] &&
0 < Subscript[t, 3] < Subscript[t, 4] &&
Subscript[t, 4] - Subscript[t, 3] <=
Subscript[t, 2] - Subscript[t, 1] && Subscript[t, obs] > 0 &&
Subscript[t, i] > 0 && Subscript[t, j] > 0 && \[Gamma] > 0 &&
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
3] < 0 <
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
4] < Subscript[t, i] - Subscript[t, j] - Subscript[t, 1] +
Subscript[t, 3] <
Subscript[t, i] - Subscript[t, j] + Subscript[t, 4] - Subscript[t,
1] && Subscript[t, low] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
3] && Subscript[t, mid1] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 2] + Subscript[t,
4] &&
Subscript[t, mid2] ==
Subscript[t, i] - Subscript[t, j] - Subscript[t, 1] + Subscript[t,
3] && Subscript[t, hig] ==
Subscript[t, i] - Subscript[t, j] + Subscript[t, 4] - Subscript[t,
1]]
截图如下：
但是似乎过于复杂，算了很久也算不出结果。我曾经计算过同样的积分在0<tlow<tmid1<tmid2<thig情况下的积分，花的时间也很长，能够算出结果，但得到的是分成多种情况的条件表达式（实际上应该有一个统一的表达式）。请问各位，应当如何设置积分和Simplify时的Assumptions，使得积分能算出结果，并且最终的表达式尽可能简单呢？多谢！
