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Mathematics
Mathematics
Problem
Suppose
A
=
∫
d
x
x
2
+
6
x
+
25
A = \int \frac{dx}{x^2 + 6x + 25}
A
=
∫
x
2
+
6
x
+
25
d
x
and
B
=
∫
d
x
x
2
−
6
x
−
27
B = \int \frac{dx}{x^2 - 6x - 27}
B
=
∫
x
2
−
6
x
−
27
d
x
. If
12
(
A
+
B
)
=
λ
⋅
tan
−
1
(
x
+
3
4
)
+
μ
⋅
ln
∣
x
−
9
x
+
3
∣
+
C
12(A + B) = \lambda \cdot \tan^{-1} \left( \frac{x+3}{4} \right) + \mu \cdot \ln \left| \frac{x-9}{x+3} \right| + C
12
(
A
+
B
)
=
λ
⋅
tan
−
1
(
4
x
+
3
)
+
μ
⋅
ln
x
+
3
x
−
9
+
C
, then the value of
(
λ
+
μ
)
(\lambda + \mu)
(
λ
+
μ
)
is .....
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