Expand the logarithmic expression $\ln\left(\frac{\sqrt{1+x^2}-1}{\sqrt{1+x^2}+1}\right)$

Step-by-step Solution

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ln
log
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sin
cos
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asin
acos
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\ln\left(\sqrt{1+x^2}-1\right)-\ln\left(\sqrt{1+x^2}+1\right)$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for x
  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • Load more...
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1

The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator

$\ln\left(\sqrt{1+x^2}-1\right)-\ln\left(\sqrt{1+x^2}+1\right)$

Final answer to the problem

$\ln\left(\sqrt{1+x^2}-1\right)-\ln\left(\sqrt{1+x^2}+1\right)$

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Function Plot

Plotting: $\ln\left(\sqrt{1+x^2}-1\right)-\ln\left(\sqrt{1+x^2}+1\right)$

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Got a different answer? Verify it!

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.

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