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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
98
Today's calculation of integral 98
Today's calculation of integral 98
Source: created by kunny
February 16, 2006
calculus
integration
logarithms
limit
calculus computations
Problem Statement
Let
I
n
=
∫
1
1
+
1
n
{
[
(
x
+
1
)
ln
x
+
1
]
e
x
(
e
x
ln
x
+
1
)
+
n
}
d
x
(
n
=
1
,
2
,
⋯
)
.
{{ \ I_n=\int_1^{1+\frac{1}{n}}\{[(x+1)\ln x+1]}e^{x(e^{x}\ln x+1)}}+n\}dx \ (n=1,2,\cdots).
I
n
=
∫
1
1
+
n
1
{[(
x
+
1
)
ln
x
+
1
]
e
x
(
e
x
l
n
x
+
1
)
+
n
}
d
x
(
n
=
1
,
2
,
⋯
)
.
Evaluate
lim
n
→
∞
I
n
n
.
{\lim_{n\to\infty}I_n^{n}}.
lim
n
→
∞
I
n
n
.
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