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

Step-by-step Solution

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Final Answer

$\frac{3}{19}\ln\left(x\right)^2+C_0$
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Step-by-step Solution

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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.

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

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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 6 times \frac{1}{19}. 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

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

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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 (6lnx/19x)dx using basic integralsSolve integral of (6lnx/19x)dx using u-substitutionSolve integral of (6lnx/19x)dx using integration by partsSolve integral of (6lnx/19x)dx 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
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

2. See formulas

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