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(3x-1)/(x^2+10x+6)
Solving integrals/ (3x-1)/(x^2+10x+6)

Integral of (3x-1)/(x^2+10x+6) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     3*x - 1      
 |  ------------- dx
 |   2              
 |  x  + 10*x + 6   
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{3 x - 1}{x^{2} + 10 x + 6}\, dx$$ 
Integral((3*x - 1*1)/(x^2 + 10*x + 6), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                    
 |                             /     2       \       ____ /     /          ____\      /          ____\\
 |    3*x - 1             3*log\6 + x  + 10*x/   8*\/ 19 *\- log\5 + x + \/ 19 / + log\5 + x - \/ 19 //
 | ------------- dx = C + -------------------- - ------------------------------------------------------
 |  2                              2                                       19                          
 | x  + 10*x + 6                                                                                       
 |                                                                                                     
/
$${{3\,\log \left(x^2+10\,x+6\right)}\over{2}}-{{8\,\log \left({{2\,x -2\,\sqrt{19}+10}\over{2\,x+2\,\sqrt{19}+10}}\right)}\over{\sqrt{19} }}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
/        ____\                   /        ____\                   /        ____\                   /        ____\                
|3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\
|- - --------|*log\6 - \/ 19 / + |- + --------|*log\6 + \/ 19 / - |- - --------|*log\5 - \/ 19 / - |- + --------|*log\5 + \/ 19 /
\2      19   /                   \2      19   /                   \2      19   /                   \2      19   /
$$-{{8\,\log \left(-{{12\,\sqrt{19}-55}\over{17}}\right)}\over{\sqrt{ 19}}}+{{8\,\log \left(-{{5\,\sqrt{19}-22}\over{3}}\right)}\over{ \sqrt{19}}}+{{3\,\log 17}\over{2}}-{{3\,\log 6}\over{2}}$$ 
=
= 
/        ____\                   /        ____\                   /        ____\                   /        ____\                
|3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\   |3   8*\/ 19 |    /      ____\
|- - --------|*log\6 - \/ 19 / + |- + --------|*log\6 + \/ 19 / - |- - --------|*log\5 - \/ 19 / - |- + --------|*log\5 + \/ 19 /
\2      19   /                   \2      19   /                   \2      19   /                   \2      19   /
$$- \left(\frac{3}{2} + \frac{8 \sqrt{19}}{19}\right) \log{\left(\sqrt{19} + 5 \right)} + \left(- \frac{8 \sqrt{19}}{19} + \frac{3}{2}\right) \log{\left(- \sqrt{19} + 6 \right)} - \left(- \frac{8 \sqrt{19}}{19} + \frac{3}{2}\right) \log{\left(- \sqrt{19} + 5 \right)} + \left(\frac{3}{2} + \frac{8 \sqrt{19}}{19}\right) \log{\left(\sqrt{19} + 6 \right)}$$
Simplify
Numerical answer [src] 
0.0234119054163882
0.0234119054163882
The graph
Integral of (3x-1)/(x^2+10x+6) dx

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

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