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Solving integrals/ (x+4)/(sqrt(x+1)+7)

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

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |      x + 4       
 |  ------------- dx
 |    _______       
 |  \/ x + 1  + 7   
 |                  
/                   
0
∫01x+4x+1+7 dx\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                                                                          
 |                                                                                        
/
∫x+4x+1+7 dx=C−7x+2(x+1)323+104x+1−728log⁡(x+1+7)−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
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-20002000
Plot the graph f(x)
The answer [src] 
                                                ___
  335          /      ___\                316*\/ 2 
- --- - 728*log\7 + \/ 2 / + 728*log(8) + ---------
   3                                          3
−728log⁡(2+7)−3353+31623+728log⁡(8)- 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
−728log⁡(2+7)−3353+31623+728log⁡(8)- 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.

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