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Similar expressions
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Integral of x*ln(x)^-2 dx

The solution

You have entered [src]

  1           
  /           
 |            
 |     x      
 |  ------- dx
 |     2      
 |  log (x)   
 |            
/             
0

$$\int\limits_{0}^{1} \frac{x}{\log{\left(x \right)}^{2}}\, dx$$

Integral(x/log(x)^2, (x, 0, 1))

Detail solution

Let $u = \log{\left(x \right)}$ .

Then let $du = \frac{dx}{x}$ and substitute $du$ :

$\int \frac{e^{2 u}}{u^{2}}\, du$
Now substitute $u$ back in:

$- \frac{\operatorname{E}_{2}\left(- 2 \log{\left(x \right)}\right)}{\log{\left(x \right)}}$
Add the constant of integration:

$- \frac{\operatorname{E}_{2}\left(- 2 \log{\left(x \right)}\right)}{\log{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- \frac{\operatorname{E}_{2}\left(- 2 \log{\left(x \right)}\right)}{\log{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 |    x             expint(2, -2*log(x))
 | ------- dx = C - --------------------
 |    2                    log(x)       
 | log (x)                              
 |                                      
/

$$2\,\Gamma\left(-1 , -2\,\log x\right)$$

Simplify

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Simplify

Numerical answer [src]

1.38019561125665e+19

1.38019561125665e+19

Use the examples entering the upper and lower limits of integration.

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Integral of x*ln(x)^-2 dx

Limits of integration:

The graph:

Piecewise:

The solution