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Solve the integral of logarithmic functions $\int\ln\left(\frac{1}{x+2}\right)dx$

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Solution

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Final Answer

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

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1

The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator

$\int\left(\ln\left(1\right)-\ln\left(x+2\right)\right)dx$

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

$\int\left(\ln\left(1\right)-\ln\left(x+2\right)\right)dx$

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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(1/(x+2)))dx. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Calculating the natural logarithm of 1. The integral of a function times a constant (-1) is equal to the constant times the integral of the function. The integral \int\ln\left(x+2\right)dx results in .

Final Answer

$\left(-x-2\right)\ln\left(x+2\right)+x+2+C_0$

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 ln(1/(x+2))dx using basic integralsSolve integral of ln(1/(x+2))dx using u-substitutionSolve integral of ln(1/(x+2))dx using integration by partsSolve integral of ln(1/(x+2))dx using tabular integration

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Plotting: $\left(-x-2\right)\ln\left(x+2\right)+x+2+C_0$

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1
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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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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

1. See formulas

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