Hello
I'm trying to find the indefinite integral of $\displaystyle x^{550} * (1-x)^{450}$.
How do I do this? I tried by parts but it seems to be about 450 iterations long! Any good substitution tricks or am I missing something?
Thanks!
Thomas
Hello
I'm trying to find the indefinite integral of $\displaystyle x^{550} * (1-x)^{450}$.
How do I do this? I tried by parts but it seems to be about 450 iterations long! Any good substitution tricks or am I missing something?
Thanks!
Thomas
No substitutions. You could try using the binomial theorem to say that $\displaystyle (1-x)^{450}= \sum_{i=0}^{450}C(450 i) (-1)^{450-i}x^i$, where C(n, i) is the binomial coefficient, which is the same as $\displaystyle \sum_{i=0}^{450} C(450,i) (-1)^ix^i$ since 450-i is odd if and only if i is.
Then $\displaystyle x^{550}(1- x)^{450}= \sum_{i=0}^{450} C(450,i) (-1)^i x^{i+ 550}$ and integrate term by term.