Solve the integral of logarithmic functions $\int\frac{1}{3}x\log \left(x\right)dx$

Step-by-step Solution

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Final answer to the problem

$\frac{2x^2\ln\left|x\right|-x^2}{12\ln\left|10\right|}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using basic integrals
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Product of Binomials with Common Term
  • FOIL Method
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The integral of a function times a constant ($\frac{1}{3}$) is equal to the constant times the integral of the function

$\frac{1}{3}\int x\log \left(x\right)dx$

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

$\frac{1}{3}\int x\log \left(x\right)dx$

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Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(x1/3log(x))dx. The integral of a function times a constant (\frac{1}{3}) is equal to the constant times the integral of the function. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Multiplying the fraction by x. Take the constant \frac{1}{\ln\left|10\right|} out of the integral.

Final answer to the problem

$\frac{2x^2\ln\left|x\right|-x^2}{12\ln\left|10\right|}+C_0$

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Function Plot

Plotting: $\frac{2x^2\ln\left(x\right)-x^2}{12\ln\left(10\right)}+C_0$

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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

See formulas (3)

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