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ln(x+1/x)
Solving integrals/ ln(x+1/x)

Integral of ln(x+1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |     /    1\   
 |  log|x + -| dx
 |     \    x/   
 |               
/                
0
$$\int\limits_{0}^{1} \log{\left(x + \frac{1}{x} \right)}\, dx$$ 
Integral(log(x + 1/x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                
 |                                                 
 |    /    1\                    /1\        /    1\
 | log|x + -| dx = C - x - 2*atan|-| + x*log|x + -|
 |    \    x/                    \x/        \    x/
 |                                                 
/
$$\int \log{\left(x + \frac{1}{x} \right)}\, dx = C + x \log{\left(x + \frac{1}{x} \right)} - x - 2 \operatorname{atan}{\left(\frac{1}{x} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     pi         
-1 + -- + log(2)
     2
$$-1 + \log{\left(2 \right)} + \frac{\pi}{2}$$ 
=
= 
     pi         
-1 + -- + log(2)
     2
$$-1 + \log{\left(2 \right)} + \frac{\pi}{2}$$ 
-1 + pi/2 + log(2)
Numerical answer [src] 
1.26394350735484
1.26394350735484
The graph
Integral of ln(x+1/x) dx

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

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