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.
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 $a,b,c,l,x,y,z$.