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Solving integrals/ 1/x(sqrt(x+3))

Integral of 1/x(sqrt(x+3)) 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 + 3    
 |  --------- dx
 |      x       
 |              
/               
0
∫01x+3x dx\int\limits_{0}^{1} \frac{\sqrt{x + 3}}{x}\, dx 
Integral(sqrt(x + 3)/x, (x, 0, 1))
The answer (Indefinite) [src] 
                                      //            /  ___   _______\                \
                                      ||   ___      |\/ 3 *\/ 3 + x |                |
  /                                   ||-\/ 3 *acoth|---------------|                |
 |                                    ||            \       3       /                |
 |   _______                          ||------------------------------  for 3 + x > 3|
 | \/ x + 3               _______     ||              3                              |
 | --------- dx = C + 2*\/ 3 + x  + 6*|<                                             |
 |     x                              ||            /  ___   _______\                |
 |                                    ||   ___      |\/ 3 *\/ 3 + x |                |
/                                     ||-\/ 3 *atanh|---------------|                |
                                      ||            \       3       /                |
                                      ||------------------------------  for 3 + x < 3|
                                      \\              3                              /
∫x+3x dx=C+2x+3+6({−3acoth⁡(3x+33)3for x+3>3−3atanh⁡(3x+33)3for x+3<3)\int \frac{\sqrt{x + 3}}{x}\, dx = C + 2 \sqrt{x + 3} + 6 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 < 3 \end{cases}\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] 
                  /    ___\
         ___      |2*\/ 3 |
oo - 2*\/ 3 *acoth|-------|
                  \   3   /
−23acoth⁡(233)+∞- 2 \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} + \infty 
=
= 
                  /    ___\
         ___      |2*\/ 3 |
oo - 2*\/ 3 *acoth|-------|
                  \   3   /
−23acoth⁡(233)+∞- 2 \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} + \infty 
oo - 2*sqrt(3)*acoth(2*sqrt(3)/3)
Numerical answer [src] 
76.6446998090096
76.6446998090096

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

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