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Integral of (x+4)/(sqrt(x+1)+7) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |      x + 4       
 |  ------------- dx
 |    _______       
 |  \/ x + 1  + 7   
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \frac{x + 4}{\sqrt{x + 1} + 7}\, dx$$
Integral((x + 4)/(sqrt(x + 1) + 7), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                                       
 |                                                                                     3/2
 |     x + 4                          /      _______\               _______   2*(x + 1)   
 | ------------- dx = -7 + C - 728*log\7 + \/ x + 1 / - 7*x + 104*\/ x + 1  + ------------
 |   _______                                                                       3      
 | \/ x + 1  + 7                                                                          
 |                                                                                        
/                                                                                         
$$\int \frac{x + 4}{\sqrt{x + 1} + 7}\, dx = C - 7 x + \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} + 104 \sqrt{x + 1} - 728 \log{\left(\sqrt{x + 1} + 7 \right)} - 7$$
The graph
The answer [src]
                                                ___
  335          /      ___\                316*\/ 2 
- --- - 728*log\7 + \/ 2 / + 728*log(8) + ---------
   3                                          3    
$$- 728 \log{\left(\sqrt{2} + 7 \right)} - \frac{335}{3} + \frac{316 \sqrt{2}}{3} + 728 \log{\left(8 \right)}$$
=
=
                                                ___
  335          /      ___\                316*\/ 2 
- --- - 728*log\7 + \/ 2 / + 728*log(8) + ---------
   3                                          3    
$$- 728 \log{\left(\sqrt{2} + 7 \right)} - \frac{335}{3} + \frac{316 \sqrt{2}}{3} + 728 \log{\left(8 \right)}$$
-335/3 - 728*log(7 + sqrt(2)) + 728*log(8) + 316*sqrt(2)/3
Numerical answer [src]
0.547121335743083
0.547121335743083

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