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(3x+4)/((9x^2)+6x-5)^(1/2)
Solving integrals/ (3x+4)/((9x^2)+6x-5)^(1/2)

Integral of (3x+4)/((9x^2)+6x-5)^(1/2) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |        3*x + 4         
 |  ------------------- dx
 |     ________________   
 |    /    2              
 |  \/  9*x  + 6*x - 5    
 |                        
/                         
0
$$\int\limits_{0}^{1} \frac{3 x + 4}{\sqrt{9 x^{2} + 6 x - 5}}\, dx$$ 
Integral((3*x + 4)/(sqrt(9*x^2 + 6*x - 1*5)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                _________________                                         
 |                                /               2       /         _________________       \
 |       3*x + 4                \/  -5 + 6*x + 9*x        |        /               2        |
 | ------------------- dx = C + -------------------- + log\6 + 6*\/  -5 + 6*x + 9*x   + 18*x/
 |    ________________                   3                                                   
 |   /    2                                                                                  
 | \/  9*x  + 6*x - 5                                                                        
 |                                                                                           
/
$$\log \left(6\,\sqrt{9\,x^2+6\,x-5}+18\,x+6\right)+{{\sqrt{9\,x^2+6 \,x-5}}\over{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                         ____       ___                     
     /          ___\   \/ 10    I*\/ 5       /         ____\
- log\6 + 6*I*\/ 5 / + ------ - ------- + log\24 + 6*\/ 10 /
                         3         3
$$-{{3\,\log \left(6\,\sqrt{5}\,i+6\right)-3\,\log \left(6\,\sqrt{10} +24\right)+\sqrt{5}\,i-\sqrt{10}}\over{3}}$$ 
=
= 
                         ____       ___                     
     /          ___\   \/ 10    I*\/ 5       /         ____\
- log\6 + 6*I*\/ 5 / + ------ - ------- + log\24 + 6*\/ 10 /
                         3         3
$$\frac{\sqrt{10}}{3} + \log{\left(6 \sqrt{10} + 24 \right)} - \log{\left(6 + 6 \sqrt{5} i \right)} - \frac{\sqrt{5} i}{3}$$
Simplify
Numerical answer [src] 
(2.08738357610232 - 1.75745864692772j)
(2.08738357610232 - 1.75745864692772j)
The graph
Integral of (3x+4)/((9x^2)+6x-5)^(1/2) dx

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

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