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

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asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\left(x+1\right)\ln\left|x+1\right|-x+C_1$
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Step-by-step Solution

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  • Product of Binomials with Common Term
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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.

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

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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+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

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

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Function Plot

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

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1
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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

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.

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