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Resolución de integrales/ x^2-2/ 5-x^2/ (3x+1)/ (3x+1)/(5-x^2-2x)

Integral de (3x+1)/(5-x^2-2x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    3*x + 1      
 |  ------------ dx
 |       2         
 |  5 - x  - 2*x   
 |                 
/                  
0
∫013x+1−2x+(5−x2) dx\int\limits_{0}^{1} \frac{3 x + 1}{- 2 x + \left(5 - x^{2}\right)}\, dx 
Integral((3*x + 1)/(5 - x^2 - 2*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //            /  ___        \                   \                       
                           ||   ___      |\/ 6 *(1 + x)|                   |                       
                           ||-\/ 6 *acoth|-------------|                   |                       
  /                        ||            \      6      /              2    |                       
 |                         ||----------------------------  for (1 + x)  > 6|        /      2      \
 |   3*x + 1               ||             6                                |   3*log\-5 + x  + 2*x/
 | ------------ dx = C + 2*|<                                              | - --------------------
 |      2                  ||            /  ___        \                   |            2          
 | 5 - x  - 2*x            ||   ___      |\/ 6 *(1 + x)|                   |                       
 |                         ||-\/ 6 *atanh|-------------|                   |                       
/                          ||            \      6      /              2    |                       
                           ||----------------------------  for (1 + x)  < 6|                       
                           \\             6                                /
∫3x+1−2x+(5−x2) dx=C+2({−6acoth⁡(6(x+1)6)6for (x+1)2>6−6atanh⁡(6(x+1)6)6for (x+1)2<6)−3log⁡(x2+2x−5)2\int \frac{3 x + 1}{- 2 x + \left(5 - x^{2}\right)}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x + 1\right)}{6} \right)}}{6} & \text{for}\: \left(x + 1\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x + 1\right)}{6} \right)}}{6} & \text{for}\: \left(x + 1\right)^{2} < 6 \end{cases}\right) - \frac{3 \log{\left(x^{2} + 2 x - 5 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9004
Trazar el gráfico f(x)
Respuesta [src] 
/      ___\                            /      ___\                  /      ___\                            /      ___\               
|3   \/ 6 | /          /       ___\\   |3   \/ 6 |    /      ___\   |3   \/ 6 | /          /       ___\\   |3   \/ 6 |    /      ___\
|- - -----|*\pi*I + log\-1 + \/ 6 // + |- + -----|*log\1 + \/ 6 / - |- - -----|*\pi*I + log\-2 + \/ 6 // - |- + -----|*log\2 + \/ 6 /
\2     6  /                            \2     6  /                  \2     6  /                            \2     6  /
−(66+32)log⁡(2+6)+(66+32)log⁡(1+6)−(32−66)(log⁡(−2+6)+iπ)+(32−66)(log⁡(−1+6)+iπ)- \left(\frac{\sqrt{6}}{6} + \frac{3}{2}\right) \log{\left(2 + \sqrt{6} \right)} + \left(\frac{\sqrt{6}}{6} + \frac{3}{2}\right) \log{\left(1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{\sqrt{6}}{6}\right) \left(\log{\left(-2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{\sqrt{6}}{6}\right) \left(\log{\left(-1 + \sqrt{6} \right)} + i \pi\right) 
=
= 
/      ___\                            /      ___\                  /      ___\                            /      ___\               
|3   \/ 6 | /          /       ___\\   |3   \/ 6 |    /      ___\   |3   \/ 6 | /          /       ___\\   |3   \/ 6 |    /      ___\
|- - -----|*\pi*I + log\-1 + \/ 6 // + |- + -----|*log\1 + \/ 6 / - |- - -----|*\pi*I + log\-2 + \/ 6 // - |- + -----|*log\2 + \/ 6 /
\2     6  /                            \2     6  /                  \2     6  /                            \2     6  /
−(66+32)log⁡(2+6)+(66+32)log⁡(1+6)−(32−66)(log⁡(−2+6)+iπ)+(32−66)(log⁡(−1+6)+iπ)- \left(\frac{\sqrt{6}}{6} + \frac{3}{2}\right) \log{\left(2 + \sqrt{6} \right)} + \left(\frac{\sqrt{6}}{6} + \frac{3}{2}\right) \log{\left(1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{\sqrt{6}}{6}\right) \left(\log{\left(-2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{\sqrt{6}}{6}\right) \left(\log{\left(-1 + \sqrt{6} \right)} + i \pi\right) 
(3/2 - sqrt(6)/6)*(pi*i + log(-1 + sqrt(6))) + (3/2 + sqrt(6)/6)*log(1 + sqrt(6)) - (3/2 - sqrt(6)/6)*(pi*i + log(-2 + sqrt(6))) - (3/2 + sqrt(6)/6)*log(2 + sqrt(6))
Respuesta numérica [src] 
0.792512067604429
0.792512067604429

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

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