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Mathematics
Mathematics
Problem
Compute the following integrals. a.
(
i
)
∫
0
∞
f
(
x
n
+
x
−
n
)
ln
x
d
x
x
=
0
(i) \int_0^\infty f(x^n + x^{-n}) \ln x \frac{dx}{x} = 0
(
i
)
∫
0
∞
f
(
x
n
+
x
−
n
)
ln
x
x
d
x
=
0
b.
(
i
i
)
∫
0
∞
f
(
x
n
+
x
−
n
)
ln
x
d
x
1
+
x
2
=
0
(ii) \int_0^\infty f(x^n + x^{-n}) \ln x \frac{dx}{1+x^2} = 0
(
ii
)
∫
0
∞
f
(
x
n
+
x
−
n
)
ln
x
1
+
x
2
d
x
=
0
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