Observation regarding integration with different algorithms

asked 2016-03-11 12:13:50 +0100

saad
13 ●3

I was going through some basic tutorials and noticed this interesting behavior.

integrate(exp(x)*sin(x) + exp(x)*cos(x), x)

with algorithm='maxima' gives

1/2*(cos(x) + sin(x))*e^x - 1/2*(cos(x) - sin(x))*e^x

rather than the simplified

e^x*sin(x)

given by algorithm='sympy'. It is the same when I use maxima or sympy by itself. Why is that? Why is maxima not simplifying the expression?

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answered 2016-03-11 22:43:35 +0100

tmonteil
27413 ●31 ●204 ●517 http://wiki.sagemath.o...

updated 2016-03-11 22:49:24 +0100

The simplification is not automatic, you can ask explicitely for it with the .full_simplify() method:

sage: e = integrate(exp(x)*sin(x) + exp(x)*cos(x), x)
sage: e
1/2*(cos(x) + sin(x))*e^x - 1/2*(cos(x) - sin(x))*e^x
sage: e.full_simplify()
e^x*sin(x)

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Thanks! This is what I needed.

saad ( 2016-03-12 08:32:01 +0100 )edit

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Asked: 2016-03-11 12:13:50 +0100

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Last updated: Mar 11 '16

Observation regarding integration with different algorithms edit