ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the integral of logarithmic functions $\int\ln\left(x+1\right)dx$

Go!
Symbolic mode
Text mode
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
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

##  Final answer to the problem

$\left(x+1\right)\ln\left|x+1\right|-x+C_1$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

The integral $\int\ln\left(x+1\right)dx$ results in $\left(x+1\right)\ln\left(x+1\right)-\left(x+1\right)$

$\left(x+1\right)\ln\left|x+1\right|-\left(x+1\right)$

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

$\left(x+1\right)\ln\left|x+1\right|-\left(x+1\right)$

Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln(x+1))dx. The integral \int\ln\left(x+1\right)dx results in \left(x+1\right)\ln\left(x+1\right)-\left(x+1\right). Simplify the product -(x+1). As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C. We can combine and rename -1 and C_0 as other constant of integration.

##  Final answer to the problem

$\left(x+1\right)\ln\left|x+1\right|-x+C_1$

##  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

SnapXam A2

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
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

###  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.