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

Step-by-step Solution

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Solution

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Final Answer

$2\sqrt{x}\ln\left(x\right)-4\sqrt{x}+C_0$
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Step-by-step Solution

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Rewrite the fraction $\frac{\ln\left(x\right)}{\sqrt{x}}$ inside the integral as the product of two functions: $\frac{1}{\sqrt{x}}\ln\left(x\right)$

$\int\frac{1}{\sqrt{x}}\ln\left(x\right)dx$

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

$\int\frac{1}{\sqrt{x}}\ln\left(x\right)dx$

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Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln(x)/(x^1/2))dx. Rewrite the fraction \frac{\ln\left(x\right)}{\sqrt{x}} inside the integral as the product of two functions: \frac{1}{\sqrt{x}}\ln\left(x\right). We can solve the integral \int\frac{1}{\sqrt{x}}\ln\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

$2\sqrt{x}\ln\left(x\right)-4\sqrt{x}+C_0$

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 (lnx/(x^0.5))dx using basic integralsSolve integral of (lnx/(x^0.5))dx using u-substitutionSolve integral of (lnx/(x^0.5))dx using integration by partsSolve integral of (lnx/(x^0.5))dx using tabular integration

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

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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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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

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