Integration

[Sastronomy]

I'm trying to integrate x⁴ / sqrt (a-x) from 0 to a

Wolfram Alpha gives:

. . .\(\displaystyle \int_0^a\, \dfrac{x^4}{\sqrt{a\, -\, x\,}}\, dx\, =\, \dfrac{256\, a^{9/2}}{315}\,\)

. . .\(\displaystyle \mbox{for }\, \Re(a)\, >\, 0\, \land\, \Im(a)\, =\, 0\)


Wolfram alpha link

I don't understand how they get this answer because if you enter x=a in the indefinite integral it becomes zero.

I've tried to solve this by doing integration by parts 4 times but this also gives me zero in the end.

 

[Ishuda]

I'm trying to integrate x⁴ / sqrt (a-x) from 0 to a


Wolfram alpha link


I don't understand how they get this answer because if you enter x=a in the indefinite integral it becomes zero.


I've tried to solve this by doing integration by parts 4 times but this also gives me zero in the end.

Suppose you had a polynomial p(x) such that
[p(x) (x-a)^1/2]' = x⁴ (x-a)^-1/2
What would the polynomial be?