Updates:
Labels: NeedsReview ness987
Comment #4 on issue 1394 by ness...@googlemail.com:
integrate(x*sqrt(1+2*x), x) can't do it yet
http://code.google.com/p/sympy/issues/detail?id=1394
This works in gsoc-3 (https://github.com/sympy/sympy/pull/543), although
not as prettily as one may hope:
In [38]: integrate(x*sqrt(1+2*x), x)
Out[38]:
3 5/2 2 5/2 5/2
4⋅x ⋅(2⋅x + 1) 8⋅x ⋅(2⋅x + 1) (2⋅x + 1)
- ───────────────── + ───────────────── + ────────────
3 2 3 2 15
- 120⋅x - 60⋅x - 120⋅x - 60⋅x
In [39]: _.diff(x)
Out[39]:
3 5/2 ⎛ 2 ⎞ 3 3/2 2
5/2 ⎛ 2 ⎞ 2 5/2 2 3/2
4⋅x ⋅(2⋅x + 1) ⋅⎝360⋅x + 120⋅x⎠ 20⋅x ⋅(2⋅x + 1) 8⋅x ⋅(2⋅x +
1) ⋅⎝360⋅x + 120⋅x⎠ 12⋅x ⋅(2⋅x + 1) 40⋅x ⋅(2⋅x + 1)
- ────────────────────────────────── - ────────────────── +
────────────────────────────────── - ────────────────── + ──────────────────
2 3
2 2 3 2
3 2
⎛ 3 2⎞ - 120⋅x - 60⋅x ⎛
3 2⎞ - 120⋅x - 60⋅x - 120⋅x - 60⋅x
⎝- 120⋅x - 60⋅x ⎠ ⎝-
120⋅x - 60⋅x ⎠
5/2 3/2
16⋅x⋅(2⋅x + 1) (2⋅x + 1)
+ ───────────────── + ────────────
3 2 3
- 120⋅x - 60⋅x
In [40]: simplify(_)
Out[40]:
⎽⎽⎽⎽⎽⎽⎽⎽⎽
x⋅╲╱ 2⋅x + 1
In [41]: simplify(_38)
Out[41]:
⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎛ 2 ⎞
╲╱ 2⋅x + 1 ⋅⎝6⋅x + x - 1⎠
──────────────────────────
15
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