There has to be a better way to compute integrals than looking at paper with vacant eyes and waiting for inspiration or...

There has to be a better way to compute integrals than looking at paper with vacant eyes and waiting for inspiration or burning a hole through paper with trial-and-error. Share your secrets with a brainlet.

Attached: integral.png (682x600, 20K)

Other urls found in this thread:

integral-table.com/
en.wikipedia.org/wiki/Leibniz_integral_rule#Other_problems_to_solve
link.springer.com/chapter/10.1007/978-3-319-00894-3_10
twitter.com/AnonBabble

Nope, integration is harder than differentiating. IIRC, this was actually shown mathematically (meta stuff, the likes of Gödel).

Way back in Freshman Calc, I had a prof who said that while any old fool can differentiate, 'Integration is an art'

Like with everything, I guess, just practice. In physics, especially, you'll find the same integrals coming up again and again, so eventually you'll just be able to knock them out without even thinking about it

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the problem is, that there are loads of stuff that cannot be integrated properly and instead you get non-trivial functions like erg(x) or Si(x) or maybe the occasional arctan(x).

it's called simpson's rule

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I have HEARD that there's an algorithm which can perform general integration. I mean, analytically, not numerically.

They tested it on a big book of integrals and found a huge number of them were wrong. Mostly typos. A plus where a minus should be. That sort of thing.

Never came across it again. Most people (except physicists and mathematicians) just brute-force it with a computer nowadays.

Try Wolfram.

You mean the Risch algorithm.
It's implemented in Wolfram alpha
The specification is about 100 pages long

Are there any integrals that aren't tabulated or given methods/algorithms to solve them?

example, integral table off google.

integral-table.com/

>integration by parts
>arctan, arcsin, etc.
>some other shit I fucked up so bad I forgot what it even is already

absolute bane of my existence in high school calc and probably will continue into college. I assume practice is really the best way to fix this, right?