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Solve the integral of logarithmic functions $\int5\ln\left(\sqrt{\frac{3}{x}}\right)dx$

Step-by-step Solution

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Final Answer

$5.246531x-\frac{5}{2}x\ln\left(x\right)+C_0$
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Step-by-step Solution

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The integral of a function times a constant ($5$) is equal to the constant times the integral of the function

$5\int\ln\left(\sqrt{\frac{3}{x}}\right)dx$

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$5\int\ln\left(\sqrt{\frac{3}{x}}\right)dx$

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Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(5ln((3/x)^1/2))dx. The integral of a function times a constant (5) is equal to the constant times the integral of the function. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a function times a constant (\frac{1}{2}) is equal to the constant times the integral of the function. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.

Final Answer

$5.246531x-\frac{5}{2}x\ln\left(x\right)+C_0$

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

Solve integral of 5ln((3/x)^0.5)dx using basic integralsSolve integral of 5ln((3/x)^0.5)dx using u-substitutionSolve integral of 5ln((3/x)^0.5)dx using integration by partsSolve integral of 5ln((3/x)^0.5)dx using tabular integration

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Plotting: $5.246531x-\frac{5}{2}x\ln\left(x\right)+C_0$

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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

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