## Indefinite Integral problem for bending moments

## 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+Dx

^{2}+Ex^{3}+Fx^{4}). 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 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

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

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

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

TTFN

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Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers

Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

There is a homework forum hosted by engineering.com: http://www.engineering.com/AskForum/aff/32.aspx

## RE: Indefinite Integral problem for bending moments

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.

ToRadicals@Normal[Integrate[%, x]]

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

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

## RE: Indefinite Integral problem for bending moments

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