# Integration analog of automatic differentiation

I was recently looking at automatic differentiation.

1. Does something like automatic differentiation exist for integration?
2. Would the integral be equivalent to something like Euler's method? (or am I thinking about it wrong?)

edit: I am looking at some inherited code that includes https://projects.coin-or.org/ADOL-C as a black box.

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With differentiation, knowledge of basic derivatives and rules for elementary compositions yields a very straightforward algorithm for computing partial derivatives. But for a function like $f(x,y)=3x^2+y$, which integral do you mean? With respect to $x$ or $y$? Both of them? Also it's easy to write down elementary compositions which have no indefinite integral, e.g. $f(x)=e^{x^2}$. Symbolically differentiation is easier, whereas numerically integration is easier (not a precise statement). – dls Feb 13 '12 at 22:46
Also, Euler's method is for solving initial value problems like $dy/dt=y$. This is different from finding an anti-derivative, that is, a function $F(y)$ such that $dF/dy=y$. – dls Feb 13 '12 at 22:55
A simple search will yield some hits. – André Nicolas Feb 13 '12 at 22:56
@AndréNicolas Would you mind providing some links? I don't believe what the poster is asking for actually exists. – dls Feb 14 '12 at 3:09