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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
163
Today's calculation of Integral 163
Today's calculation of Integral 163
Source: created by kunny
October 21, 2006
calculus
integration
trigonometry
calculus computations
Problem Statement
Let
I
n
=
∫
0
π
4
tan
n
x
d
x
(
n
=
0
,
1
,
2
,
⋯
)
.
I_{n}=\int_{0}^{\frac{\pi}{4}}\tan^{n}x\ dx\ (n=0,\ 1,\ 2,\ \cdots).
I
n
=
∫
0
4
π
tan
n
x
d
x
(
n
=
0
,
1
,
2
,
⋯
)
.
Find
∑
n
=
0
∞
{
I
n
+
2
2
+
(
I
n
+
1
+
I
n
+
3
)
I
n
+
2
+
I
n
+
1
I
n
+
3
}
.
\sum_{n=0}^{\infty}\{{I_{n+2}}^{2}+(I_{n+1}+I_{n+3})I_{n+2}+I_{n+1}I_{n+3}\}.
∑
n
=
0
∞
{
I
n
+
2
2
+
(
I
n
+
1
+
I
n
+
3
)
I
n
+
2
+
I
n
+
1
I
n
+
3
}
.
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