$$\int_0^\infty \left( 1 - \left(1 - e^{-\frac{2x}{24}}\right)^{11}\left(1 - e^{-\frac{x}{24}}\right)\left(1 - e^{-\frac{x}{72}}\right)^{2}\left(1 - e^{-\frac{2x}{144}}\right)^{2} \right) \ dx$$
Hey Guys!!
- I have been trying to integrate the above question but cannot do it because it is too long and therefore, needs to be done by a computer (as it over 50+ terms!!!)
- The problem is that i do not have my computer software which can do it for me so i thought you guys can help me out by doing it.
- If you have a smarter way, i am all ears.
Thank you so much :)
The integral evaluates to
$$\frac{19179385249735728551550367428216940591727383888374120235641}{80577616728959000543177737840861586668464761577474749000}$$ $$\approx 238.02373448509798.$$
Such computations can usually be carried out on Wolfram Alpha (click here for mobile version).
Alternatively you could try the substitution suggested in the comments ($u=e^{x/144}$).