# Integration of the binomial theorem

1. Dec 8, 2008

### hmmmmm

is it possible to integrate the binomial theorem??

2. Dec 8, 2008

### tiny-tim

Welcome to PF!

Hiho hmmmmm! Welcome to PF!
Yes, and that should give you an equation relating nCk and n-1Ck-1

what is it?

3. Dec 8, 2008

### HallsofIvy

Staff Emeritus
What do you mean by "integrating a theorem", integrating both sides of the equation involved? If so, yes, tiny-tim is correct.

4. Dec 10, 2008

### hmmmmm

ok so what would happen if you integrated both sides of it then.

5. Dec 10, 2008

### tiny-tim

uh-uh … you tell us!

6. Dec 10, 2008

### HallsofIvy

Staff Emeritus
1) Write down the formula for "the binomial theorem."

2) Integrate each side separately. That shouldn't be difficult, they both involve just the "power rule", that the integral of xn is (1/n+1)xn+1+ a constant.

What do you get?

7. Dec 11, 2008

### hmmmmm

yes this is the part i dont understand how you would integrate (a^x+B)^y once expanded not in the braket.

8. Dec 11, 2008

### HallsofIvy

Staff Emeritus
"(a^x+ B)^y is NOT a binomial form. Do you mean (Ax+ B)^y where A, B, and y are constants? If so, do not expand it. Make the substitution u= Ax+ B so that du= Adx and dx= (1/A)du.

9. Dec 12, 2008

### hmmmmm

i mean the integral of (a^x+b)^y da where x b and y are constants sorry for my sloppy notation

10. Dec 12, 2008

### HallsofIvy

Staff Emeritus
Good! So do what we have been encouraging you do to all along! Write out (a^x+ b)^y in terms of the binomial expansion and integrate, term by term.