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Resolución de integrales/ x*x+1/ 2/(-3*x*x+10*x+1)

Integral de 2/(-3*x*x+10*x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |          2           
 |  ----------------- dx
 |  -3*x*x + 10*x + 1   
 |                      
/                       
0
∫012(−3xx+10x)+1 dx\int\limits_{0}^{1} \frac{2}{\left(- 3 x x + 10 x\right) + 1}\, dx 
Integral(2/((-3*x)*x + 10*x + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                //            /    ___           \                         \
                                ||   ___      |3*\/ 7 *(-5/3 + x)|                         |
                                ||-\/ 7 *acoth|------------------|                         |
  /                             ||            \        14        /                 2       |
 |                              ||---------------------------------  for (-5/3 + x)  > 28/9|
 |         2                    ||                42                                       |
 | ----------------- dx = C - 6*|<                                                         |
 | -3*x*x + 10*x + 1            ||            /    ___           \                         |
 |                              ||   ___      |3*\/ 7 *(-5/3 + x)|                         |
/                               ||-\/ 7 *atanh|------------------|                         |
                                ||            \        14        /                 2       |
                                ||---------------------------------  for (-5/3 + x)  < 28/9|
                                \\                42                                       /
∫2(−3xx+10x)+1 dx=C−6({−7acoth⁡(37(x−53)14)42for (x−53)2>289−7atanh⁡(37(x−53)14)42for (x−53)2<289)\int \frac{2}{\left(- 3 x x + 10 x\right) + 1}\, dx = C - 6 \left(\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} \left(x - \frac{5}{3}\right)}{14} \right)}}{42} & \text{for}\: \left(x - \frac{5}{3}\right)^{2} > \frac{28}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} \left(x - \frac{5}{3}\right)}{14} \right)}}{42} & \text{for}\: \left(x - \frac{5}{3}\right)^{2} < \frac{28}{9} \end{cases}\right)
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9004
Trazar el gráfico f(x)
Respuesta [src] 
        /          /        ___\\            /          ___\         /          /        ___\\            /          ___\
    ___ |          |2   2*\/ 7 ||     ___    |  5   2*\/ 7 |     ___ |          |5   2*\/ 7 ||     ___    |  2   2*\/ 7 |
  \/ 7 *|pi*I + log|- + -------||   \/ 7 *log|- - + -------|   \/ 7 *|pi*I + log|- + -------||   \/ 7 *log|- - + -------|
        \          \3      3   //            \  3      3   /         \          \3      3   //            \  3      3   /
- ------------------------------- - ------------------------ + ------------------------------- + ------------------------
                 14                            14                             14                            14
7log⁡(−23+273)14−7log⁡(−53+273)14−7(log⁡(23+273)+iπ)14+7(log⁡(53+273)+iπ)14\frac{\sqrt{7} \log{\left(- \frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \log{\left(- \frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(\frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} 
=
= 
        /          /        ___\\            /          ___\         /          /        ___\\            /          ___\
    ___ |          |2   2*\/ 7 ||     ___    |  5   2*\/ 7 |     ___ |          |5   2*\/ 7 ||     ___    |  2   2*\/ 7 |
  \/ 7 *|pi*I + log|- + -------||   \/ 7 *log|- - + -------|   \/ 7 *|pi*I + log|- + -------||   \/ 7 *log|- - + -------|
        \          \3      3   //            \  3      3   /         \          \3      3   //            \  3      3   /
- ------------------------------- - ------------------------ + ------------------------------- + ------------------------
                 14                            14                             14                            14
7log⁡(−23+273)14−7log⁡(−53+273)14−7(log⁡(23+273)+iπ)14+7(log⁡(53+273)+iπ)14\frac{\sqrt{7} \log{\left(- \frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \log{\left(- \frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(\frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} 
-sqrt(7)*(pi*i + log(2/3 + 2*sqrt(7)/3))/14 - sqrt(7)*log(-5/3 + 2*sqrt(7)/3)/14 + sqrt(7)*(pi*i + log(5/3 + 2*sqrt(7)/3))/14 + sqrt(7)*log(-2/3 + 2*sqrt(7)/3)/14
Respuesta numérica [src] 
0.523227442378083
0.523227442378083

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

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