can someone guide me through a process of using a CAS to solve an integration problem that goes through a specific point? I have never been allowed to use a CAS for a class and now the homework specifically tells me to use one. I have access to wolfram alpha pro, if I can use that

Question

chrisplusian · Answer

Use a computer algebra system to determine the antiderivative that passes through the given point. Use the system to graph the resulting antiderivative......$$\int\limits \frac{ x^3 }{ (x^2 -4)^2 } dx$$

chrisplusian · Answer

(3,4)

chrisplusian · Answer

Do you have a minute @Algebraic! ??

chrisplusian · Answer

do you know how to do this? is it something that can be explained without seeing the calculator or wolfram? @Algebraic! ???

anonymous · Answer

hmm not sure.  Is this from a chapter titled something like "antiderivatives, differential equations and modeling"  ..?

chrisplusian · Answer

No this is from "partial fractions" section 8.5 of larson and edwards ninth edition calculus. problem number 36 to be exact :)

anonymous · Answer

really...?
hmm

chrisplusian · Answer

I have no problem with the first part:) I know how to use wolfram to get an indefinite integral... but then I have no clue what to do

anonymous · Answer

not sure what they're alluding to... let me look through a textbook for some problems that might be similar...
meanwhile ...
@Hero  or @eSpeX  
might have an idea.

anonymous · Answer

ah, think I found one actually...  let me look it over.

chrisplusian · Answer

k

espex · Answer

You should be able to solve the integral with your CAS and then plug in your values to solve for C. Once done you should have all the unknowns solved for and if both sides of the equation are equal, then it passes through that point.

anonymous · Answer

yeah I think that's actually all it wants you to do... I was thinking it wanted you to reduce the differential equation to an algebra equation, but I think all it is saying is "use wolfram to integrate"  (lol)

chrisplusian · Answer

what would you plug the y value into???? do you just plug in the values of "x"? then after you have the "c" then set it all equal to the "y" value and solve to check?

anonymous · Answer

this is dy = (x^3/(x^2-4)^2 ) dx

anonymous · Answer

integrate both sides.... y= F(x) +C  plug in the value given to find C

chrisplusian · Answer

aha!!! that makes sense thank you for your help

anonymous · Answer

sure, sorry for the confusion... "CAS" threw me off... thought they wanted you to do something tricky or something:)
credit goes to @eSpeX