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Solving integrals/ (4sqrt(1-x)-sqrt(3x+1))/(sqrt(3x+1)+4sqrt(1-x))

Integral of (4sqrt(1-x)-sqrt(3x+1))/(sqrt(3x+1)+4sqrt(1-x)) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1                             
  /                             
 |                              
 |      _______     _________   
 |  4*\/ 1 - x  - \/ 3*x + 1    
 |  ------------------------- dx
 |    _________       _______   
 |  \/ 3*x + 1  + 4*\/ 1 - x    
 |                              
/                               
0
$$\int\limits_{0}^{1} \frac{4 \sqrt{1 - x} - \sqrt{3 x + 1}}{4 \sqrt{1 - x} + \sqrt{3 x + 1}}\, dx$$ 
Integral((4*sqrt(1 - x) - sqrt(3*x + 1))/(sqrt(3*x + 1) + 4*sqrt(1 - x)), (x, 0, 1))
The answer [src] 
  1                               
  /                               
 |                                
 |      _________       _______   
 |  - \/ 1 + 3*x  + 4*\/ 1 - x    
 |  --------------------------- dx
 |     _________       _______    
 |   \/ 1 + 3*x  + 4*\/ 1 - x     
 |                                
/                                 
0
$$\int\limits_{0}^{1} \frac{4 \sqrt{1 - x} - \sqrt{3 x + 1}}{4 \sqrt{1 - x} + \sqrt{3 x + 1}}\, dx$$ 
=
= 
  1                               
  /                               
 |                                
 |      _________       _______   
 |  - \/ 1 + 3*x  + 4*\/ 1 - x    
 |  --------------------------- dx
 |     _________       _______    
 |   \/ 1 + 3*x  + 4*\/ 1 - x     
 |                                
/                                 
0
$$\int\limits_{0}^{1} \frac{4 \sqrt{1 - x} - \sqrt{3 x + 1}}{4 \sqrt{1 - x} + \sqrt{3 x + 1}}\, dx$$ 
Integral((-sqrt(1 + 3*x) + 4*sqrt(1 - x))/(sqrt(1 + 3*x) + 4*sqrt(1 - x)), (x, 0, 1))
Numerical answer [src] 
0.216224142712758
0.216224142712758

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

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