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# Integrate the function $\ln\left(1+x\right)$ from 0 to $1$

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ln
log
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lim
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sin
cos
tan
cot
sec
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asin
acos
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sinh
cosh
tanh
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sech
csch

asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$2\ln\left(2\right)-1$
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##  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
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1

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

$\left[\left(\left(x+1\right)\ln\left|x+1\right|-\left(x+1\right)\right)\right]_{0}^{1}$

Learn how to solve definite integrals problems step by step online.

$\left[\left(\left(x+1\right)\ln\left|x+1\right|-\left(x+1\right)\right)\right]_{0}^{1}$

Learn how to solve definite integrals problems step by step online. Integrate the function ln(1+x) from 0 to 1. The integral \int\ln\left(1+x\right)dx results in \left(x+1\right)\ln\left(x+1\right)-\left(x+1\right). Simplify the product -(x+1). Evaluate the definite integral. Simplify the expression.

##  Final answer to the problem

$2\ln\left(2\right)-1$

##  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

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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

###  Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b