4
votes
0answers
83 views

Symbolic math engines barf on this ostensibly tractable integral.

$$\frac14 \int_{-M\pi}^{N\pi - s} \cos(tu/M) \cos((t+s)u/M)(1-\cos(t/M))(1-\cos((t+s)/N))\space \mathrm d t$$ with integer $u$. Alpha runs out of time. Maxima gives a tremendous result that can ...
0
votes
0answers
168 views

Symbolic integration of vector norm

I'd like to symbolically integrate the expression $\int_0^1{\|r'\left(t\right)\|_2\,dt}$ where $r$ is a function $\mathbb{R} \rightarrow \mathbb{R}^2$ (so the expression is the arc length of the curve ...
1
vote
3answers
93 views

Find symbolic integral for expression containing multivariate polynomials

I'm looking for a way to symbolically integrate the following expression (the $k_i$ are integer constants): Using a generalized form of the identity I was able to express it without the ...
1
vote
0answers
83 views

Why are some integrals not analytically solvable? [duplicate]

Possible Duplicate: How can you prove that a function has no closed form integral? (Forgive my crude lingo) Why do some integrals seem to be unsolvable; that is to say the indefinite ...
37
votes
3answers
950 views

How much does symbolic integration mean to mathematics?

(Before reading, I apologize for my poor English ability.) I have enjoyed calculating some symbolic integrals as a hobby, and this has been one of the main source of my interest towards the vast ...