Solve the integral of logarithmic functions $\int\frac{\sqrt{4-\ln\left(x\right)}}{x}dx$

Used Formulas

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e
π
ln
log
log
lim
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sin
cos
tan
cot
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asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Power Rule of Integration
$\int x^ndx=\frac{x^{\left(n+1\right)}}{n+1}+C$

Function Plot

Plotting: $-\frac{2}{3}\sqrt{\left(4-\ln\left(x\right)\right)^{3}}+C_0$

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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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