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sqrt(x+4)/x
Solving integrals/ sqrt(x+4)/x

Integral of sqrt(x+4)/x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |    _______   
 |  \/ x + 4    
 |  --------- dx
 |      x       
 |              
/               
0
∫01x+4x dx\int\limits_{0}^{1} \frac{\sqrt{x + 4}}{x}\, dx 
Integral(sqrt(x + 4)/x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                             
 |                                                                              
 |   _______                                                                    
 | \/ x + 4                /      _______\       _______        /       _______\
 | --------- dx = C - 2*log\2 + \/ 4 + x / + 2*\/ 4 + x  + 2*log\-2 + \/ 4 + x /
 |     x                                                                        
 |                                                                              
/
∫x+4x dx=C+2x+4+2log⁡(x+4−2)−2log⁡(x+4+2)\int \frac{\sqrt{x + 4}}{x}\, dx = C + 2 \sqrt{x + 4} + 2 \log{\left(\sqrt{x + 4} - 2 \right)} - 2 \log{\left(\sqrt{x + 4} + 2 \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-2000020000
Plot the graph f(x)
The answer [src] 
            /  ___\
            |\/ 5 |
oo - 4*acoth|-----|
            \  2  /
−4acoth⁡(52)+∞- 4 \operatorname{acoth}{\left(\frac{\sqrt{5}}{2} \right)} + \infty 
=
= 
            /  ___\
            |\/ 5 |
oo - 4*acoth|-----|
            \  2  /
−4acoth⁡(52)+∞- 4 \operatorname{acoth}{\left(\frac{\sqrt{5}}{2} \right)} + \infty 
oo - 4*acoth(sqrt(5)/2)
Numerical answer [src] 
88.4236637667497
88.4236637667497
The graph
Integral of sqrt(x+4)/x dx

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

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