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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of cosx
- Integral of ln|x|
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Integral of x*sin(x)^2
- Integral of x^n*e^(-x)
- Derivative of:
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ln|x|
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Identical expressions
- ln|x|
- ln module of x|
- ln|x|dx
Integral of ln|x| dx
The solution
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[src]
1 / | | log(|x|) dx | / 0
$$\int\limits_{0}^{1} \log{\left(\left|{x}\right| \right)}\, dx$$
Integral(log(|x|), (x, 0, 1))
The answer (Indefinite)
[src]
/ /
| |
| d | d
/ | --(im(x))*im(x)*sign(x) | --(re(x))*re(x)*sign(x)
| | dx | dx
| log(|x|) dx = C - | ----------------------- dx - | ----------------------- dx + x*log(|x|)
| | |x| | |x|
/ | |
/ /
$$\int \log{\left(\left|{x}\right| \right)}\, dx = C + x \log{\left(\left|{x}\right| \right)} - \int \frac{\operatorname{re}{\left(x\right)} \operatorname{sign}{\left(x \right)} \frac{d}{d x} \operatorname{re}{\left(x\right)}}{\left|{x}\right|}\, dx - \int \frac{\operatorname{im}{\left(x\right)} \operatorname{sign}{\left(x \right)} \frac{d}{d x} \operatorname{im}{\left(x\right)}}{\left|{x}\right|}\, dx$$
Use the examples entering the upper and lower limits of integration.