Integrate the function $\log_{2}\left(x^4-1\right)$

Step-by-step Solution

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Final answer to the problem

$\frac{\left(x^4-1\right)\ln\left|x^4-1\right|-x^4+1}{\ln\left|2\right|}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Find the integral

$\int\log_{2}\left(x^4-1\right)dx$

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$\int\log_{2}\left(x^4-1\right)dx$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Integrate the function log2(x^4+-1). Find the integral. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Take the constant \frac{1}{\ln\left|2\right|} out of the integral. The integral \int\ln\left(x^4-1\right)dx results in \left(x^4-1\right)\ln\left(x^4-1\right)-\left(x^4-1\right).

Final answer to the problem

$\frac{\left(x^4-1\right)\ln\left|x^4-1\right|-x^4+1}{\ln\left|2\right|}+C_0$

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Function Plot

Plotting: $\frac{\left(x^4-1\right)\ln\left(x^4-1\right)-x^4+1}{\ln\left(2\right)}+C_0$

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1
2
3
4
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

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