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Solving integrals/ (sqrt(3x+1))/(sqrt(3x+1)+5)

Integral of (sqrt(3x+1))/(sqrt(3x+1)+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |      _________     
 |    \/ 3*x + 1      
 |  --------------- dx
 |    _________       
 |  \/ 3*x + 1  + 5   
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{\sqrt{3 x + 1}}{\sqrt{3 x + 1} + 5}\, dx$$ 
Integral(sqrt(3*x + 1)/(sqrt(3*x + 1) + 5), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                         
 |                                                                          
 |     _________                         _________         /      _________\
 |   \/ 3*x + 1         1           10*\/ 1 + 3*x    50*log\5 + \/ 1 + 3*x /
 | --------------- dx = - + C + x - -------------- + -----------------------
 |   _________          3                 3                     3           
 | \/ 3*x + 1  + 5                                                          
 |                                                                          
/
$$\int \frac{\sqrt{3 x + 1}}{\sqrt{3 x + 1} + 5}\, dx = C + x - \frac{10 \sqrt{3 x + 1}}{3} + \frac{50 \log{\left(\sqrt{3 x + 1} + 5 \right)}}{3} + \frac{1}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  7   50*log(6)   50*log(7)
- - - --------- + ---------
  3       3           3
$$- \frac{50 \log{\left(6 \right)}}{3} - \frac{7}{3} + \frac{50 \log{\left(7 \right)}}{3}$$ 
=
= 
  7   50*log(6)   50*log(7)
- - - --------- + ---------
  3       3           3
$$- \frac{50 \log{\left(6 \right)}}{3} - \frac{7}{3} + \frac{50 \log{\left(7 \right)}}{3}$$ 
-7/3 - 50*log(6)/3 + 50*log(7)/3
Numerical answer [src] 
0.235844663787638
0.235844663787638

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

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