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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
- Integral of ((1+x)^2)^(1/3)
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Integral of x/(x^2+4)^(1/2)
- Integral of x/sqrt(x^2-4x+1)
- Integral of (x)/(x^3-1)
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Identical expressions
- ln(one + one /x)
- ln(1 plus 1 divide by x)
- ln(one plus one divide by x)
- ln1+1/x
- ln(1+1 divide by x)
- ln(1+1/x)dx
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Similar expressions
- ln(1-1/x)
- ln(1+1/x^(1/2))/(2*x(1/2))
- ln(1+(1/x))/(x(x-1)^(1/5))
- ln(1+(1/x))/(x*(x-1)^(1/4))
Integral of ln(1+1/x) dx
The solution
You have entered
[src]
1 / | | / 1\ | log|1 + -| dx | \ x/ | / 0
$$\int\limits_{0}^{1} \log{\left(1 + \frac{1}{x} \right)}\, dx$$
Integral(log(1 + 1/x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | / 1\ /2\ / 1\ / 2\ | log|1 + -| dx = C - log|-| + x*log|1 + -| + log|2 + -| | \ x/ \x/ \ x/ \ x/ | /
$$\int \log{\left(1 + \frac{1}{x} \right)}\, dx = C + x \log{\left(1 + \frac{1}{x} \right)} - \log{\left(\frac{2}{x} \right)} + \log{\left(2 + \frac{2}{x} \right)}$$
The graph
The answer
[src]
2*log(2)
$$2 \log{\left(2 \right)}$$
=
=
2*log(2)
$$2 \log{\left(2 \right)}$$
2*log(2)
The graph
Use the examples entering the upper and lower limits of integration.