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Resolución de integrales/ 2-x^2/ ln(2-x^2)

Integral de ln(2-x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 11               
 --               
 10               
  /               
 |                
 |     /     2\   
 |  log\2 - x / dx
 |                
/                 
0
∫01110log⁡(2−x2) dx\int\limits_{0}^{\frac{11}{10}} \log{\left(2 - x^{2} \right)}\, dx 
Integral(log(2 - x^2), (x, 0, 11/10))
Respuesta (Indefinida) [src] 
                          //            /    ___\             \                      
                          ||   ___      |x*\/ 2 |             |                      
                          ||-\/ 2 *acoth|-------|             |                      
  /                       ||            \   2   /        2    |                      
 |                        ||----------------------  for x  > 2|                      
 |    /     2\            ||          2                       |              /     2\
 | log\2 - x / dx = C - 4*|<                                  | - 2*x + x*log\2 - x /
 |                        ||            /    ___\             |                      
/                         ||   ___      |x*\/ 2 |             |                      
                          ||-\/ 2 *atanh|-------|             |                      
                          ||            \   2   /        2    |                      
                          ||----------------------  for x  < 2|                      
                          \\          2                       /
∫log⁡(2−x2) dx=C+xlog⁡(2−x2)−2x−4({−2acoth⁡(2x2)2for x2>2−2atanh⁡(2x2)2for x2<2)\int \log{\left(2 - x^{2} \right)}\, dx = C + x \log{\left(2 - x^{2} \right)} - 2 x - 4 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases}\right)
Simplificar
Gráfica
0.01.10.10.20.30.40.50.60.70.80.91.01-1
Trazar el gráfico f(x)
Respuesta [src] 
             / 79\                                                                                                          
       11*log|---|                                                                                                          
  11         \100/     ___ /          /  ___\\     ___    /11     ___\     ___ /          /  11     ___\\     ___    /  ___\
- -- + ----------- + \/ 2 *\pi*I + log\\/ 2 // + \/ 2 *log|-- + \/ 2 | - \/ 2 *|pi*I + log|- -- + \/ 2 || - \/ 2 *log\\/ 2 /
  5         10                                            \10        /         \          \  10        //
−115−2log⁡(2)+11log⁡(79100)10+2log⁡(1110+2)−2(log⁡(−1110+2)+iπ)+2(log⁡(2)+iπ)- \frac{11}{5} - \sqrt{2} \log{\left(\sqrt{2} \right)} + \frac{11 \log{\left(\frac{79}{100} \right)}}{10} + \sqrt{2} \log{\left(\frac{11}{10} + \sqrt{2} \right)} - \sqrt{2} \left(\log{\left(- \frac{11}{10} + \sqrt{2} \right)} + i \pi\right) + \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) 
=
= 
             / 79\                                                                                                          
       11*log|---|                                                                                                          
  11         \100/     ___ /          /  ___\\     ___    /11     ___\     ___ /          /  11     ___\\     ___    /  ___\
- -- + ----------- + \/ 2 *\pi*I + log\\/ 2 // + \/ 2 *log|-- + \/ 2 | - \/ 2 *|pi*I + log|- -- + \/ 2 || - \/ 2 *log\\/ 2 /
  5         10                                            \10        /         \          \  10        //
−115−2log⁡(2)+11log⁡(79100)10+2log⁡(1110+2)−2(log⁡(−1110+2)+iπ)+2(log⁡(2)+iπ)- \frac{11}{5} - \sqrt{2} \log{\left(\sqrt{2} \right)} + \frac{11 \log{\left(\frac{79}{100} \right)}}{10} + \sqrt{2} \log{\left(\frac{11}{10} + \sqrt{2} \right)} - \sqrt{2} \left(\log{\left(- \frac{11}{10} + \sqrt{2} \right)} + i \pi\right) + \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) 
-11/5 + 11*log(79/100)/10 + sqrt(2)*(pi*i + log(sqrt(2))) + sqrt(2)*log(11/10 + sqrt(2)) - sqrt(2)*(pi*i + log(-11/10 + sqrt(2))) - sqrt(2)*log(sqrt(2))
Respuesta numérica [src] 
0.481763983885695
0.481763983885695

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

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