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Mathematics
Problem
If
I
(
x
)
=
∫
3
d
x
(
4
x
+
6
)
(
4
x
2
+
8
x
+
3
)
I(x) = \int \frac{3dx}{(4x+6)(\sqrt{4x^2+8x+3})}
I
(
x
)
=
∫
(
4
x
+
6
)
(
4
x
2
+
8
x
+
3
)
3
d
x
where
I
(
0
)
=
3
4
+
20
I(0) = \frac{\sqrt{3}}{4} + 20
I
(
0
)
=
4
3
+
20
and
I
(
1
2
)
=
a
2
b
+
c
I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b} + c
I
(
2
1
)
=
b
a
2
+
c
, for
a
,
b
,
c
∈
N
a, b, c \in \mathbb{N}
a
,
b
,
c
∈
N
,
gcd
(
a
,
b
)
=
1
\gcd(a, b) = 1
g
cd
(
a
,
b
)
=
1
,
a
+
b
+
c
a + b + c
a
+
b
+
c
is equal to
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