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Mathematics
Mathematics
Problem
∫
1
1
−
e
2
x
d
x
=
\int \frac{1}{\sqrt{1-e^{2x}}}\,dx =
∫
1
−
e
2
x
1
d
x
=
(a)
x
−
log
[
1
+
1
−
e
2
x
]
+
c
x - \log[1 + \sqrt{1-e^{2x}}] + c
x
−
lo
g
[
1
+
1
−
e
2
x
]
+
c
(b)
x
+
log
[
1
+
1
−
e
2
x
]
+
c
x + \log[1 + \sqrt{1-e^{2x}}] + c
x
+
lo
g
[
1
+
1
−
e
2
x
]
+
c
(c)
log
[
1
+
1
−
e
2
x
]
−
x
+
c
\log[1 + \sqrt{1-e^{2x}}] - x + c
lo
g
[
1
+
1
−
e
2
x
]
−
x
+
c
(d) None of these (a)
x
−
log
[
1
+
1
−
e
2
x
]
+
c
x - \log[1 + \sqrt{1-e^{2x}}] + c
x
−
lo
g
[
1
+
1
−
e
2
x
]
+
c
(b)
x
+
log
[
1
+
1
−
e
2
x
]
+
c
x + \log[1 + \sqrt{1-e^{2x}}] + c
x
+
lo
g
[
1
+
1
−
e
2
x
]
+
c
(c)
log
[
1
+
1
−
e
2
x
]
−
x
+
c
\log[1 + \sqrt{1-e^{2x}}] - x + c
lo
g
[
1
+
1
−
e
2
x
]
−
x
+
c
(d) None of these
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