Computer Algebra System that Can Integrate this Function

• Apr 3rd 2013, 02:21 PM
Philly2034
Computer Algebra System that Can Integrate this Function
For some reason, wolfram alpha does not seem to understand integration.

http://www.wolframalpha.com/input/?i=(1%2FL)*((integrate+(a_1*x^2%2Ba_2*x%2Ba_3)*(co s(n*pi*x%2FL)+from+-L+to+0)%2B(integrate+(b_1*x^2%2Bb_2*x%2Bb_3)*(cos( n*pi*x%2FL)++from+0+to+L))

Is there a computer algebra system that can integrate
(1/L)*((integrate (a_1*x^2+a_2*x+a_3)*(cos(n*pi*x/L) from -L to 0)+(integrate (b_1*x^2+b_2*x+b_3)*(cos(n*pi*x/L) from 0 to L))
• Apr 3rd 2013, 02:30 PM
Ruun
Re: Computer Algebra System that Can Integrate this Function
You will probably be able to do it with Maple. Can you LaTeX (LaTeX - Wikipedia, the free encyclopedia) the integrals that you want?

My guess is

$\frac{1}{L}\left( \int_{-L}^0\left( a_{1}x^2+a_{2}x+a_{3}\right) \cos\left( \frac{n \pi x}{L}\right)dx +\int_{0}^{L}\left(b_{1}x^2+b_{2}x+b_{3} \right)\cos\left( \frac{n \pi x}{L}\right)dx \right)$

To do that integral I will first re-scale $x$ to $u_{n}=\frac{n \pi x}{L}$ and then integrate by parts two times in order to lower the grade of the polynomial. A little of brute force but it works just fine.
• Apr 3rd 2013, 09:04 PM
zzephod
Re: Computer Algebra System that Can Integrate this Function
Quote:

Originally Posted by Philly2034
For some reason, wolfram alpha does not seem to understand integration.

http://www.wolframalpha.com/input/?i=(1%2FL)*((integrate+(a_1*x^2%2Ba_2*x%2Ba_3)*(co s(n*pi*x%2FL)+from+-L+to+0)%2B(integrate+(b_1*x^2%2Bb_2*x%2Bb_3)*(cos( n*pi*x%2FL)++from+0+to+L))

Is there a computer algebra system that can integrate
(1/L)*((integrate (a_1*x^2+a_2*x+a_3)*(cos(n*pi*x/L) from -L to 0)+(integrate (b_1*x^2+b_2*x+b_3)*(cos(n*pi*x/L) from 0 to L))

Why not try it with properly matched parentheses, also break it down into smaller parts.

.