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Solve the integral of logarithmic functions $\int-2\ln\left(x\right)^3dx$

Step-by-step Solution

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Final Answer

$-2x\ln\left(x\right)^3-12x\ln\left(x\right)+12x+6x\ln\left(x\right)^{2}+C_0$
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Step-by-step Solution

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The integral of a function times a constant ($-2$) is equal to the constant times the integral of the function

$-2\int\ln\left(x\right)^3dx$

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

$-2\int\ln\left(x\right)^3dx$

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Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(-2ln(x)^3)dx. The integral of a function times a constant (-2) is equal to the constant times the integral of the function. We can solve the integral \int\ln\left(x\right)^3dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

$-2x\ln\left(x\right)^3-12x\ln\left(x\right)+12x+6x\ln\left(x\right)^{2}+C_0$

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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 -2lnx^3dx using basic integralsSolve integral of -2lnx^3dx using u-substitutionSolve integral of -2lnx^3dx using integration by partsSolve integral of -2lnx^3dx using tabular integration

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Plotting: $-2x\ln\left(x\right)^3-12x\ln\left(x\right)+12x+6x\ln\left(x\right)^{2}+C_0$

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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

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

4. See formulas

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