illustrate with fixed n
choose n :
n
1
2
3
4
5
integrand:
x
n
x
n
x
sin(x)
n
x
cos(x)
n
sin
(x)
n
tan
(x)
n
log
(x)
n
x
x+1
To establish a reduction formula for
x
n
x
dx,use integration by parts:
u =
n
x
dv =
x
dx
du = n
n-1
x
dx
v =
x
x
n
x
dx =
x
n
x
- n
x
n-1
x
dx
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