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

Step-by-step Solution

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Solution

Formulas

Videos

Final Answer

$x\ln\left(x\right)-x+C_0$
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Step-by-step Solution

Problem to solve:

$\int\ln\left(x\right)dx$

Specify the solving method

1

We can solve the integral $\int\ln\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=\ln\left(x\right)}\\ \displaystyle{du=\frac{1}{x}dx}\end{matrix}$

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

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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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))dx. We can solve the integral \int\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. Solve the integral.

Final Answer

$x\ln\left(x\right)-x+C_0$

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 int(ln(x))dx using basic integralsSolve int(ln(x))dx using u-substitutionSolve int(ln(x))dx using integration by partsSolve int(ln(x))dx using tabular integration
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Go!
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
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

How to improve your answer:

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$\int\ln\left(x\right)dx$

Main topic:

Integrals involving Logarithmic Functions

Used formulas:

4. See formulas

Time to solve it:

~ 0.04 s

Related topics:

Integrals involving Logarithmic FunctionsIntegral CalculusCalculusBasic Differentiation RulesFactorizationIntegration by PartsIntegration Techniques

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