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

Step-by-step Solution

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Final Answer

$\frac{3}{4}x^{4}\ln\left(x\right)-\frac{3}{16}x^{4}+C_0$
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Step-by-step Solution

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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$\int3x^3\ln\left(x\right)dx$

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

$\int3x^3\ln\left(x\right)dx$

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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^3ln(x^3))dx. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a function times a constant (3) is equal to the constant times the integral of the function. We can solve the integral \int x^3\ln\left(x\right)dx 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.

Final Answer

$\frac{3}{4}x^{4}\ln\left(x\right)-\frac{3}{16}x^{4}+C_0$

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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 x^3ln(x^3)dx using basic integralsSolve integral of x^3ln(x^3)dx using u-substitutionSolve integral of x^3ln(x^3)dx using integration by partsSolve integral of x^3ln(x^3)dx using tabular integration

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Plotting: $\frac{3}{4}x^{4}\ln\left(x\right)-\frac{3}{16}x^{4}+C_0$

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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

3. See formulas

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