Q
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Answer:
By parts.
Explanation:
You can integrate it by parts with the rule
∫
f
'
(
x
)
g
(
x
)
d
x
=
f
(
x
)
g
(
x
)
−
∫
f
(
x
)
g
'
(
x
)
where we assume that
f
'
(
x
)
=
1
and
g
(
x
)
=
ln
(
x
+
√
x
2
+
1
)
consequently
f
(
x
)
=
x
and
g
'
(
x
)
=
1
√
x
2
+
1
.
The integral is then
∫
ln
(
x
+
√
x
2
+
1
)
d
x
=
x
ln
(
x
+
√
x
2
+
1
)
−
∫
x
√
x
2
+
1
d
x
=
x
ln
(
x
+
√
x
2
+
1
)
−
√
x
2
+
1
+
C
.
Step-by-step explanation:
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