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Solving integrals/ 1/(log(x+2)/log(e))

Integral of 1/(log(x+2)/log(e)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  /log(x + 2)\   
 |  |----------|   
 |  \  log(E)  /   
 |                 
/                  
0
$$\int\limits_{0}^{\infty} \frac{1}{\frac{1}{\log{\left(e \right)}} \log{\left(x + 2 \right)}}\, dx$$ 
Integral(1/(log(x + 2)/log(E)), (x, 0, oo))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

      LiRule(a=1, b=2, context=1/log(x + 2), symbol=x)

    Method #2

    1. Rewrite the integrand:

      LiRule(a=1, b=2, context=1/log(x + 2), symbol=x)

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                                
 |      1                         
 | ------------ dx = C + li(2 + x)
 | /log(x + 2)\                   
 | |----------|                   
 | \  log(E)  /                   
 |                                
/
$$\int \frac{1}{\frac{1}{\log{\left(e \right)}} \log{\left(x + 2 \right)}}\, dx = C + \operatorname{li}{\left(x + 2 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo - li(2)
$$- \operatorname{li}{\left(2 \right)} + \infty$$ 
=
= 
oo - li(2)
$$- \operatorname{li}{\left(2 \right)} + \infty$$ 
oo - li(2)

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

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