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Resolución de integrales/ (3x+5)/ (3x+5)/(x^2+6x+4)

Integral de (3x+5)/(x^2+6x+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    3*x + 5      
 |  ------------ dx
 |   2             
 |  x  + 6*x + 4   
 |                 
/                  
0
∫013x+5(x2+6x)+4 dx\int\limits_{0}^{1} \frac{3 x + 5}{\left(x^{2} + 6 x\right) + 4}\, dx 
Integral((3*x + 5)/(x^2 + 6*x + 4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //            /  ___        \                   \                      
                           ||   ___      |\/ 5 *(3 + x)|                   |                      
                           ||-\/ 5 *acoth|-------------|                   |                      
  /                        ||            \      5      /              2    |                      
 |                         ||----------------------------  for (3 + x)  > 5|        /     2      \
 |   3*x + 5               ||             5                                |   3*log\4 + x  + 6*x/
 | ------------ dx = C - 4*|<                                              | + -------------------
 |  2                      ||            /  ___        \                   |            2         
 | x  + 6*x + 4            ||   ___      |\/ 5 *(3 + x)|                   |                      
 |                         ||-\/ 5 *atanh|-------------|                   |                      
/                          ||            \      5      /              2    |                      
                           ||----------------------------  for (3 + x)  < 5|                      
                           \\             5                                /
∫3x+5(x2+6x)+4 dx=C−4({−5acoth⁡(5(x+3)5)5for (x+3)2>5−5atanh⁡(5(x+3)5)5for (x+3)2<5)+3log⁡(x2+6x+4)2\int \frac{3 x + 5}{\left(x^{2} + 6 x\right) + 4}\, dx = C - 4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x + 3\right)}{5} \right)}}{5} & \text{for}\: \left(x + 3\right)^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x + 3\right)}{5} \right)}}{5} & \text{for}\: \left(x + 3\right)^{2} < 5 \end{cases}\right) + \frac{3 \log{\left(x^{2} + 6 x + 4 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
/        ___\                  /        ___\                  /        ___\                  /        ___\               
|3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\
|- - -------|*log\4 - \/ 5 / + |- + -------|*log\4 + \/ 5 / - |- - -------|*log\3 - \/ 5 / - |- + -------|*log\3 + \/ 5 /
\2      5   /                  \2      5   /                  \2      5   /                  \2      5   /
−(255+32)log⁡(5+3)−(32−255)log⁡(3−5)+(32−255)log⁡(4−5)+(255+32)log⁡(5+4)- \left(\frac{2 \sqrt{5}}{5} + \frac{3}{2}\right) \log{\left(\sqrt{5} + 3 \right)} - \left(\frac{3}{2} - \frac{2 \sqrt{5}}{5}\right) \log{\left(3 - \sqrt{5} \right)} + \left(\frac{3}{2} - \frac{2 \sqrt{5}}{5}\right) \log{\left(4 - \sqrt{5} \right)} + \left(\frac{2 \sqrt{5}}{5} + \frac{3}{2}\right) \log{\left(\sqrt{5} + 4 \right)} 
=
= 
/        ___\                  /        ___\                  /        ___\                  /        ___\               
|3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\   |3   2*\/ 5 |    /      ___\
|- - -------|*log\4 - \/ 5 / + |- + -------|*log\4 + \/ 5 / - |- - -------|*log\3 - \/ 5 / - |- + -------|*log\3 + \/ 5 /
\2      5   /                  \2      5   /                  \2      5   /                  \2      5   /
−(255+32)log⁡(5+3)−(32−255)log⁡(3−5)+(32−255)log⁡(4−5)+(255+32)log⁡(5+4)- \left(\frac{2 \sqrt{5}}{5} + \frac{3}{2}\right) \log{\left(\sqrt{5} + 3 \right)} - \left(\frac{3}{2} - \frac{2 \sqrt{5}}{5}\right) \log{\left(3 - \sqrt{5} \right)} + \left(\frac{3}{2} - \frac{2 \sqrt{5}}{5}\right) \log{\left(4 - \sqrt{5} \right)} + \left(\frac{2 \sqrt{5}}{5} + \frac{3}{2}\right) \log{\left(\sqrt{5} + 4 \right)} 
(3/2 - 2*sqrt(5)/5)*log(4 - sqrt(5)) + (3/2 + 2*sqrt(5)/5)*log(4 + sqrt(5)) - (3/2 - 2*sqrt(5)/5)*log(3 - sqrt(5)) - (3/2 + 2*sqrt(5)/5)*log(3 + sqrt(5))
Respuesta numérica [src] 
0.925252223761184
0.925252223761184

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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