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

Step-by-step Solution

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Final answer to the problem

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

How should I solve this problem?

  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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Change the logarithm to base $e$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$

$\int\left(\frac{\ln\left(x\right)}{\ln\left(10\right)}\right)^2dx$

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$\int\left(\frac{\ln\left(x\right)}{\ln\left(10\right)}\right)^2dx$

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Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(log(x)^2)dx. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Take the constant \frac{1}{\ln\left|10\right|^2} out of the integral. We can solve the integral \int\ln\left(x\right)^2dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.

Final answer to the problem

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

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Function Plot

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

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1
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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

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