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Solving integrals/ (9x^2-1-√(3x-1))/(3x+1)

Integral of (9x^2-1-√(3x-1))/(3x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                          
  /                          
 |                           
 |     2         _________   
 |  9*x  - 1 - \/ 3*x - 1    
 |  ---------------------- dx
 |         3*x + 1           
 |                           
/                            
0
$$\int\limits_{0}^{1} \frac{- \sqrt{3 x - 1} + \left(9 x^{2} - 1\right)}{3 x + 1}\, dx$$ 
Integral((9*x^2 - 1 - sqrt(3*x - 1))/(3*x + 1), (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
                                              /  ___\
                                     ___      |\/ 2 |
        ___              ___   2*I*\/ 2 *atanh|-----|
1   2*\/ 2    2*I   pi*\/ 2                   \  2  /
- - ------- + --- + -------- - ----------------------
2      3       3       6                 3
$$- \frac{2 \sqrt{2}}{3} + \frac{1}{2} + \frac{\sqrt{2} \pi}{6} - \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{2}}{2} \right)}}{3} + \frac{2 i}{3}$$ 
=
= 
                                              /  ___\
                                     ___      |\/ 2 |
        ___              ___   2*I*\/ 2 *atanh|-----|
1   2*\/ 2    2*I   pi*\/ 2                   \  2  /
- - ------- + --- + -------- - ----------------------
2      3       3       6                 3
$$- \frac{2 \sqrt{2}}{3} + \frac{1}{2} + \frac{\sqrt{2} \pi}{6} - \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{2}}{2} \right)}}{3} + \frac{2 i}{3}$$ 
1/2 - 2*sqrt(2)/3 + 2*i/3 + pi*sqrt(2)/6 - 2*i*sqrt(2)*atanh(sqrt(2)/2)/3
Numerical answer [src] 
(0.297795864044104 - 0.164094118405237j)
(0.297795864044104 - 0.164094118405237j)

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

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