Updates:
Status: Duplicate
Labels: Integration
Mergedinto: 1304
Comment #1 on issue 2483 by asmeurer: integrate problem
http://code.google.com/p/sympy/issues/detail?id=2483
Sorry, but integration of algebraic functions is very limited in SymPy
right now. It can do this one if you give it the sign of a, i.e.,
In [3]: a = Symbol('a', positive=True)
In [4]: integrate(sqrt(x**2 + a**2), x)
Out[4]:
2 ⎛x⎞ ⎽⎽⎽⎽⎽⎽⎽⎽⎽
a ⋅asinh⎜─⎟ ╱ 2 2
⎝a⎠ x⋅╲╱ a + x
─────────── + ──────────────
2 2
In [5]: a = Symbol('a', negative=True)
In [6]: integrate(sqrt(x**2 + a**2), x)
Out[6]:
2 ⎛x⎞ ⎽⎽⎽⎽⎽⎽⎽⎽⎽
a ⋅asinh⎜─⎟ ╱ 2 2
⎝a⎠ x⋅╲╱ a + x
- ─────────── + ──────────────
2 2
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