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# Indefinite Integral problem for bending moments2

## Indefinite Integral problem for bending moments

(OP)
Using MathCAD 14.0, I am trying to take the indefinite integral and double integral of moment-curvature equations in the form of Ax/(B+Cx+Dx2+Ex3+Fx4). If I attempt this with the symbolic equal sign, it churns for a while, turns red, and says "out of memory". If I attempt this with the Symbolics>Variable menu, it churns for a while, then freezes up. Is a different version (or program) better suited for this integral? If I had the general solution, I could work out the A,B,C,D,E, and F values for each beam separately. I am running 32-bit Vista with 4GB ram.

### RE: Indefinite Integral problem for bending moments

I have given up on Mathcad am using Mathematica instead. What I have found is that even Mathematica will use up all of 16GB of ram. My suspicions is that Mathcad doesn't have a chance with less memory.

I don't see two variables to integrate so how can you do a double integral?

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Indefinite Integral problem for bending moments

(OP)
Peter,

Thanks for the response. I was just considering learning MATLAB, but maybe I should give Mathematica a look instead. Is one better with symbolic integrals?

With bending equations, the integral of M(x) is Theta(x) and the integral of that is v(x) (deflection). Both integrations are w.r.t x.

### RE: Indefinite Integral problem for bending moments

Have you tried Wolfram Alpha?
http://www.wolframalpha.com/input/?i=integral%28in...

It looks too messy to solve by hand

TTFN
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### RE: Indefinite Integral problem for bending moments

I tried using Mathematica. There is no limit for x. If x could be integrated over a range then Mathematica can solve numerically but then just about anything can solve numerically.

In[2]:= Integrate[(Z*x)/(B + C*x + D*x^2 + E*x^3 + F*x^4), x]

Out[2]= Z RootSum[
B + C #1 + D #1^2 + E #1^3 + F #1^4 &, (Log[x - #1] #1)/(
C + 2 D #1 + 3 E #1^2 + 4 F #1^3) &]

I tried integrating with respect to x again and I got a similar looking answer in the denominator and the numerator added a few more terms.

I am not even sure what RootSum means. I need to look that up.

This looks like a tuff one. You could try sci.math.symbolic there are some experienced Mathematica heavy weights there.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Indefinite Integral problem for bending moments

While the integral solution might be cute for a report, why you need to have the indefinite integral solved? A numerical solution would seem to suffice in most cases, if not all.

TTFN
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### RE: Indefinite Integral problem for bending moments

This is what works
ToRadicals@Normal[Integrate[(A*x)/(B + C*x + D*x^2 + E*x^3 + F*x^4), x]]
The answer is VERY loooooong. There are a lot of repeated terms that could be solved and then substituted but it would take a lot of work. I could only figure out how to get the output in MathML or LaTex form.

The answer to the second integal is even longer.

I did get answers but whether they are that useful is another matter. Like I said there are a lot of places where a square root term is used in many places.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Indefinite Integral problem for bending moments

I figured out how to save the results to a text file.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Indefinite Integral problem for bending moments

Not every expression has got a "closed form" indefinite integral.
In fact very few of them do.
If you were to think of a random expression, the chance of it having a "closed form" indefinite integral are very miniscule indeed.

The misconception, that there is a closed form answer are rooted in the problem solving we do at pre university level, where the questions are
contrived ones.
In fact, the whole terminology is wrong.We are asked to "solve" for an indefinite integral, in fact we dont, what we normally do
is to guess an answer(from memory) and refactor it to produce the right answer.
On the other hand you can "solve" for diffrentiation, since an algorithmic procedure exists .There is no such thing for indefinite integral, only a hotch potch of methods
which allow for an intelligent hunch for solution.

Hence it is no surprise MathCAD fails in this regard for many an expression.
Mathematica is a lot advanced in this regard,but don't assume that you would get an answer for each and every integral that you can think of.

### RE: Indefinite Integral problem for bending moments

(OP)
Thank you guys for all of the help. IRstuff and PNachtwey, after your recommendations I got a copy of Mathematica and rewrote my equations and inputs that I was attempting in MathCAD. IRstuff, good call on having it crunch a numerical solution sooner rather than later. By using DSolve w/ FullSimplify, I was able to add a lot more detail than I was even expecting to get and it handles the many integrals and boundary conditions no problem! Couple days of learning curve but its working great now - thank you.

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