Need to work on some other stuff soon, so falling back on this one I had prepared a while ago for such an occasion.Can you solve this integral?∫01(1+x4)20084x3(1+x4(2006))dx= ?Previous iteration: #746521 (answer in #746671).
This is as far as I got. Maybe someone else can take it the rest of the way
The left term can be easily calculated.
For the right term, let
Using integration by parts, you can show that:
Starting at F(0) which is easy to calculate, you can use the above algorithm to eventually calculate F(2006) to find the answer.
For the right term, one can do another substitution. Will write it out later.
See here: #750702
First, break the integral into two parts as
Using the u=1+x4 substitution, the first integral becomes
while the second becomes
With the additional substitution v=1−1/u, the final integral above becomes
so that the original integral is equal to
Curious as to how the hint was related
Ah i was trying to hint at the fact one had to do another substitution. You had already done one, i was trying to tell you to do another one. Instead of switching to integration by parts. Maybe not the best hint ;)
I'm sticking with 42. It's going to be correct eventually.
Just for you, I'll make sure that it'll happen, one day... just need to stick around, long enough
I'll do my best!
Hint: never change a winning team...
I bet it's greater than zero and less than one! Ahhhah