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# Solve the integral of logarithmic functions $\int\frac{6\ln\left(x\right)}{19x}dx$

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##  Final answer to the problem

$\frac{3}{19}\ln\left|x\right|^2+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

Take out the constant $6$ from the integral

$6\int\frac{\ln\left(x\right)}{19x}dx$

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

$6\int\frac{\ln\left(x\right)}{19x}dx$

Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int((6ln(x))/(19x))dx. Take out the constant 6 from the integral. Take the constant \frac{1}{19} out of the integral. Multiply the fraction and term in 6\cdot \left(\frac{1}{19}\right)\int\frac{\ln\left(x\right)}{x}dx. We can solve the integral \int\frac{\ln\left(x\right)}{x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \ln\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

##  Final answer to the problem

$\frac{3}{19}\ln\left|x\right|^2+C_0$

##  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

SnapXam A2

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1
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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

###  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.