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

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Solution

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Final Answer

$\frac{x^{3}\ln\left(x\right)}{3}-\frac{1}{9}x^{3}+C_0$
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Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

We can solve the integral $\int x^2\ln\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Unlock the first 2 steps of this solution.

Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(x^2ln(x))dx. We can solve the integral \int x^2\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. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{x^{3}\ln\left(x\right)}{3}-\frac{1}{9}x^{3}+C_0$

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^2lnxdx using basic integralsSolve integral of x^2lnxdx using u-substitutionSolve integral of x^2lnxdx using integration by partsSolve integral of x^2lnxdx using tabular integration

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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
D□x
∫
∫◻
|◻|
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:

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Main topic:

Integrals involving Logarithmic Functions

Used formulas:

2. See formulas

Related topics:

Integrals involving Logarithmic FunctionsIntegral CalculusCalculusLogarithmic DifferentiationBasic Differentiation RulesFactorizationIntegration by PartsIntegration Techniques

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