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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 2/x^4
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Integral of arcsinxdx
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Integral of (x)/(1+x^2)
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Integral of 2x*e^x^2
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Identical expressions
- one /(x*log(x- two)^ two)
- 1 divide by (x multiply by logarithm of (x minus 2) squared )
- one divide by (x multiply by logarithm of (x minus two) to the power of two)
- 1/(x*log(x-2)2)
- 1/x*logx-22
- 1/(x*log(x-2)²)
- 1/(x*log(x-2) to the power of 2)
- 1/(xlog(x-2)^2)
- 1/(xlog(x-2)2)
- 1/xlogx-22
- 1/xlogx-2^2
- 1 divide by (x*log(x-2)^2)
- 1/(x*log(x-2)^2)dx
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Similar expressions
- 1/(x*log(x+2)^2)
Integral of 1/(x*log(x-2)^2) dx
The solution
You have entered
[src]
1 / | | 1 | ------------- dx | 2 | x*log (x - 2) | / 0
$$\int\limits_{0}^{1} \frac{1}{x \log{\left(x - 2 \right)}^{2}}\, dx$$
Integral(1/(x*log(x - 2)^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ / | | | 1 | 1 2 - x | ------------- dx = C + 2* | -------------- dx + ------------- | 2 | 2 x*log(-2 + x) | x*log (x - 2) | x *log(-2 + x) | | / /
$$\int \frac{1}{x \log{\left(x - 2 \right)}^{2}}\, dx = C + 2 \int \frac{1}{x^{2} \log{\left(x - 2 \right)}}\, dx + \frac{2 - x}{x \log{\left(x - 2 \right)}}$$
The answer
[src]
1
/
|
/ 1 \ | 1 I
- oo*sign|-------------| + 2* | -------------- dx - --
\pi*I + log(2)/ | 2 pi
| x *log(-2 + x)
|
/
0
$$2 \int\limits_{0}^{1} \frac{1}{x^{2} \log{\left(x - 2 \right)}}\, dx - \frac{i}{\pi} - \infty \operatorname{sign}{\left(\frac{1}{\log{\left(2 \right)} + i \pi} \right)}$$
=
=
1
/
|
/ 1 \ | 1 I
- oo*sign|-------------| + 2* | -------------- dx - --
\pi*I + log(2)/ | 2 pi
| x *log(-2 + x)
|
/
0
$$2 \int\limits_{0}^{1} \frac{1}{x^{2} \log{\left(x - 2 \right)}}\, dx - \frac{i}{\pi} - \infty \operatorname{sign}{\left(\frac{1}{\log{\left(2 \right)} + i \pi} \right)}$$
-oo*sign(1/(pi*i + log(2))) + 2*Integral(1/(x^2*log(-2 + x)), (x, 0, 1)) - i/pi
Numerical answer
[src]
(-3.88142669314496 - 1.76129664103813j)
(-3.88142669314496 - 1.76129664103813j)
Use the examples entering the upper and lower limits of integration.