I'm struggling with some integrals which one of them looks like THIS:

$\displaystyle{\int_0^{3.8}\frac{\pi^4 x y (a+9 c+8 b \cos(\frac{\pi z}{l})+18 c \cos(\frac{2 \pi z}{l})) \sin^2(\frac{\pi z}{l})}{l^4} dz}$

I just need a result but unfortunately wolframalpha and integral-calculator can't hold this integral. Of course, I can split it into several parts but then the result becomes unpleasantly long. Is there any software that can calculate this and other massive definite integrals?

By the way, coefficients "x", "y" and "l" are already calculated but "a", "b" and "c" - undetermined.

  • 1
    $\begingroup$ WolframAlpha do all the job only if you pay. But you can ask for only a part of the job (do not specify the limits of integration) wolframalpha.com/input/… Then, with the formula, you can introduce the values of the boundaries by yourself. $\endgroup$ – JJacquelin May 24 '14 at 11:22
  • $\begingroup$ @JJacquelin Oh! I already calculated this integral without boundaries. When I saw the result, I thought that further calculation will become total mess. After your comment I looked again and now I understand that all those sin values becomes 0 if I define z as 0 or 3.8 because l=3.8. Thank you anyway! :) $\endgroup$ – Ramekin May 24 '14 at 17:12

Assuming that I properly typed the integrand $$\frac{\pi ^4 x y \left(a+8 b \cos \left(\frac{\pi z}{l}\right)+18 c \sin ^2\left(\frac{\pi z}{l}\right) \cos \left(\frac{2 \pi z}{l}\right)+9 c\right)}{l^4}$$ the antiderivative is $$\frac{\pi ^3 x y \left(4 \pi z (2 a+9 c)+64 b l \sin \left(\frac{\pi z}{l}\right)-9 c l \left(\sin \left(\frac{4 \pi z}{l}\right)-4 \sin \left(\frac{2 \pi z}{l}\right)\right)\right)}{8 l^4}$$ which is equal to $0$ if $z=0$. So plug your numbers for $a,b,c,l,x,y,z$.


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