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

Step-by-step Solution

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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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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.

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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0
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(◻)
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◻/◻
/
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◻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: 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

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