$\int_{0}^{1}\ln\left(1+x\right)dx$

Step-by-step Solution

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Final answer to the problem

$\left(1+1\right)\ln\left|1+1\right|- 1-1-\left(\left(0+1\right)\ln\left|0+1\right|- 0-1\right)$
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Step-by-step Solution

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Apply the formula: $\int\ln\left(x+b\right)dx$$=\left(x+b\right)\ln\left(x+b\right)-\left(x+b\right)+C$, where $b=1$ and $x+b=1+x$

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

Learn how to solve intégrales définies problems step by step online.

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

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Learn how to solve intégrales définies problems step by step online. int(ln(1+x))dx&0&1. Apply the formula: \int\ln\left(x+b\right)dx=\left(x+b\right)\ln\left(x+b\right)-\left(x+b\right)+C, where b=1 and x+b=1+x. Apply the formula: -\left(a+b\right)=-a-b, where a=x, b=1, -1.0=-1 and a+b=x+1. Apply the formula: \left[x\right]_{a}^{b}=eval\left(x,b\right)-eval\left(x,a\right)+C, where a=0, b=1 and x=\left(x+1\right)\ln\left(x+1\right)-x-1.

Final answer to the problem

$\left(1+1\right)\ln\left|1+1\right|- 1-1-\left(\left(0+1\right)\ln\left|0+1\right|- 0-1\right)$

Exact Numeric Answer

$0.386294$

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Function Plot

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

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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

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