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Mathematics
Mathematics
Problem
If
f
(
x
)
=
ln
(
−
x
+
x
2
+
1
)
f(x) = \ln(-x + \sqrt{x^2 + 1})
f
(
x
)
=
ln
(
−
x
+
x
2
+
1
)
, then
∫
f
′
′
(
x
)
d
x
\int f''(x)\,dx
∫
f
′′
(
x
)
d
x
is equal to - (A)
1
(
x
+
x
2
+
1
)
+
c
\frac{1}{(x + \sqrt{x^2 + 1})} + c
(
x
+
x
2
+
1
)
1
+
c
(B)
−
1
x
2
+
1
+
c
\frac{-1}{\sqrt{x^2 + 1}} + c
x
2
+
1
−
1
+
c
(C)
−
x
2
+
1
+
c
-\sqrt{x^2 + 1} + c
−
x
2
+
1
+
c
(D)
ln
(
x
+
x
2
+
1
)
\ln(x + \sqrt{x^2 + 1})
ln
(
x
+
x
2
+
1
)
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