hmmm ..... they should be equal, but !!!

Question

amistre64 · Answer

why arent they? http://www.wolframalpha.com/input/?i=%28x^3%2B5%29^10%2F30 http://www3.wolframalpha.com/input/?i=sum%28n%3D0+to+9%29+%28%289%21%285^%289-n%29%29%28x^%283n%2B3%29%29%2F%28%28n%21%29%289-n%29%21%283n%2B3%29%29

amistre64 · Answer

they appear to differ only by a constant

anonymous · Answer

how were the p's?  minted?

amistre64 · Answer

they was what they were :)  didnt sweat it :)

anonymous · Answer

one is from 0 to ten, the other from 0 to 9 for one thing

amistre64 · Answer

when I integrate:

$$\int x^2(x^3+5)^9dx=\frac{1}{30}(x^3+5)^{10}+C$$
$$\int \sum_{0}^{9} C(9,n)\ 5^{9-n}\ x^{3n+3}\ dx=\sum_{0}^{9} C(9,n)\ 5^{9-n}\ \frac{x^{3n+3}}{3n+2}+C$$

amistre64 · Answer

they have the same derivative :)  but the result differ by a constant .... i find that rather scintilatting

amistre64 · Answer

is it cause one is discrete?

anonymous · Answer

how can they differ by a constant when you already have a constant in your answer???

amistre64 · Answer

lol .... when i dont put on the +C, they two are like sec^2 and tan^2+1

anonymous · Answer

makes you appreciate exponential notation more