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Solve the integral of logarithmic functions $\int\left(\frac{x^3}{\sqrt{x^4-1}}-\ln\left(4\right)\right)dx$

Step-by-step Solution

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Final Answer

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

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Simplify the expression inside the integral

$\int\frac{x^3}{\sqrt{x^4-1}}dx+\int-\ln\left(4\right)dx$

Learn how to solve integrals involving logarithmic functions problems step by step online.

$\int\frac{x^3}{\sqrt{x^4-1}}dx+\int-\ln\left(4\right)dx$

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Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int((x^3)/((x^4-1)^1/2)-ln(4))dx. Simplify the expression inside the integral. The integral \int\frac{x^3}{\sqrt{x^4-1}}dx results in: \frac{1}{2}\sqrt{x^4-1}. The integral \int-\ln\left(4\right)dx results in: -\ln\left(4\right)x. Gather the results of all integrals.

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of ((x^3)/((x^4-1)^0.5)+-1ln4)dx using basic integralsSolve integral of ((x^3)/((x^4-1)^0.5)+-1ln4)dx using u-substitutionSolve integral of ((x^3)/((x^4-1)^0.5)+-1ln4)dx using integration by partsSolve integral of ((x^3)/((x^4-1)^0.5)+-1ln4)dx using tabular integration

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Function Plot

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

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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: Integrals involving Logarithmic Functions

They are those integrals where the function that we are integrating is composed only of combinations of logarithmic functions.

Used Formulas

3. See formulas

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