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Putnam
1941 Putnam
A2
A2
Part of
1941 Putnam
Problems
(1)
Putnam 1941 A2
Source: Putnam 1941
2/23/2022
Find the
n
n
n
-th derivative with respect to
x
x
x
of
∫
0
x
(
1
+
x
−
t
1
!
+
(
x
−
t
)
2
2
!
+
…
+
(
x
−
t
)
n
−
1
(
n
−
1
)
!
)
e
n
t
d
t
.
\int_{0}^{x} \left(1+\frac{x-t}{1!}+\frac{(x-t)^{2}}{2!}+\ldots+\frac{(x-t)^{n-1}}{(n-1)!}\right)e^{nt} dt.
∫
0
x
(
1
+
1
!
x
−
t
+
2
!
(
x
−
t
)
2
+
…
+
(
n
−
1
)!
(
x
−
t
)
n
−
1
)
e
n
t
d
t
.
Putnam
calculus
derivative