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Integral Trouble

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I''m doing som spare-time maths studying, but unfortunately, my general math skills seems to have deteriorated somewhat. I''m having some problems resolving "larger" integrals. Examples: Integral( sqrt(a + bx^n + cx^m) dx ) Integral( sqrt(a + bx^n + cx^m) * (d + x^o) dx ) Are there any general rules applying here? Something similar/opposite to derivation product and core rules? Any online resources / integration rules would be appreciated! (I''m aware of mathworld, but I''m not quite sure what to look for, there''s like 60 integral topics there :-| ) -meZ

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If you looked hard enough on mathworld, you would have found the basic Integration rules at http://mathworld.wolfram.com/Integral.html

Edited by - core on November 13, 2001 2:02:29 PM

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What I found here is:

Chebyshev proved that if U, V, and W are rational numbers, then
Integral( x^u(A+Bx^v)^w dx )

is integrable in terms of elementary functions (if (u+1)/v, w, or w+(u+1)/v is an integer)

This I could work with, but how would I go about actually solving such an integration?

-meZ

Edited by - meZmo on November 13, 2001 3:25:10 PM

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Guest Anonymous Poster
You''d have to try some kind of trigonometric subsitituiton for the value inside the root...

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Guest Anonymous Poster
Also you can look for tables, and try a reduction method...

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Thanks AP!

I''ll give trig. subst. a try.

What do you mean by "look for tables and try a reduction method"? Do you mean look for "known" integrals and subst. for those?

-meZ

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Guest Anonymous Poster
its hard to do an integral of something in a root,(or raised toan exponent) if you are unable to find some kind of trig relationship, or if it is a nice integral that you can you integration by parts, so far complex mathematical/engineering integrals, some kind of integral exists that can continually reduce the expression to something simpler to integrate through repeated integration... something to that effect...
a little shaky with my integral calculus tho...

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Well I always understood integration to be part of the basics of calculus, and i just had an exam on that and i seemed to kick mucho ass, but here''s my stab at answering your question on integration/anti-differentiation. striaght from the maths book:
For example, if f''(x) = 2x then f(x) = 2x^2/2 = x^2

Rule 2. If f''(x) = ax^n, then antiderivative is
f(x) = ax^(n + 1)/(n + 1) + c, n != -1, where c is a constant

and with square roots and stuff, just convert them to there positive exponent form and apply the rule, hope that helped, cya.

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Guest Anonymous Poster
but that wont work if you''re integrating a polynomial expression raised to an exponent wrt to the variable of the polynomial...

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You had trouble with that integral? Geez, you must be some kind of dip You might want to look for something related to numeric integration such as Simpson''s rule. You might also want to review the definition of the integral and rheiman sums.

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