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∫
0
∞
(
sin
(
x
)
x
)
3
d
x
\displaystyle \int_0^{\infty} \left(\frac{\sin(x)}{x}\right)^3 \, dx
∫
0
∞
(
x
sin
(
x
)
)
3
d
x
Borwein Integral (Sinc^3)
∫
0
∞
cos
(
x
)
x
2
+
1
d
x
\displaystyle \int_0^{\infty} \frac{\cos(x)}{x^2 + 1} \, dx
∫
0
∞
x
2
+
1
cos
(
x
)
d
x
Recall classic integrals
∫
0
1
arctan
(
2
+
x
2
)
(
x
2
+
1
)
2
+
x
2
d
x
\displaystyle \int\limits_0^1 \frac{\arctan(\sqrt{2+x^2})}{(x^2 + 1)\sqrt{2+x^2}} \, dx
0
∫
1
(
x
2
+
1
)
2
+
x
2
arctan
(
2
+
x
2
)
d
x
Fix Wolfram Mathematica failure
∑
n
=
1
∞
(
−
1
)
n
ln
(
1
+
1
n
)
\displaystyle \sum_{n=1}^{\infty} (-1)^n \ln{\left( 1+\frac{1}{n} \right)}
n
=
1
∑
∞
(
−
1
)
n
ln
(
1
+
n
1
)
Discover sum
3
128
(
56
5
−
125
)
3
F
2
(
3
2
,
3
2
,
3
2
;
2
,
2
;
1
128
(
47
−
21
5
)
)
+
4
(
5
5
−
1
)
K
(
1
32
(
16
−
7
3
−
15
)
)
2
π
2
\frac{3}{128} (56 \sqrt{5}-125) _3F_2 \left(\frac{3}{2},\frac{3}{2},\frac{3}{2};2,2;\frac{1}{128} (47-21 \sqrt{5} ) \right)+\frac{4 (5 \sqrt{5}-1) K(\frac{1}{32} (16-7 \sqrt{3}-\sqrt{15}))^2}{\pi^2}
128
3
(
56
5
−
125
)
3
F
2
(
2
3
,
2
3
,
2
3
;
2
,
2
;
128
1
(
47
−
21
5
)
)
+
π
2
4
(
5
5
−
1
)
K
(
32
1
(
16
−
7
3
−
15
)
)
2
Simplify expressions