Help with Integration: θ/(θ+2) from x=0 to 1

[bpschn01]

Hi,

I am told that:
θ(θ+1)∫x^θ(1-x)dx = θ/(θ+2)
∫ from x=0 to 1
Would someone be so kind as to show me how, or give me some tips.

This is a small part of a solution for a statistical problem I'm trying to understand.
Thank you ...

 

[JJacquelin]

(x^t)(1-x) = (x^t) - (x^(t+1))
You know how to integrate (x^t) , i suppose.

 

[Mark44]

Hi,

I am told that:
θ(θ+1)∫x^θ(1-x)dx = θ/(θ+2)
∫ from x=0 to 1
Would someone be so kind as to show me how, or give me some tips.

This is a small part of a solution for a statistical problem I'm trying to understand.
Thank you ...

In more readable form, and with θ replaced by t, the equation is
$$ t(t + 1) \int_0^1 x^t(1 - x)dx = \frac{t}{t + 2}$$

 

[bpschn01]

Thanks JJacquelin! It's the simple stuff that gets me.