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Resolución de integrales/ 4*x^2/ sqrt(2)/ 1/(sqrt(2)-4*x^2)

Integral de 1/(sqrt(2)-4*x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |    ___      2   
 |  \/ 2  - 4*x    
 |                 
/                  
0
∫011−4x2+2 dx\int\limits_{0}^{1} \frac{1}{- 4 x^{2} + \sqrt{2}}\, dx 
Integral(1/(sqrt(2) - 4*x^2), (x, 0, 1))
Solución detallada

    PieceweseRule(subfunctions=[(ArctanRule(a=1, b=-4, c=sqrt(2), context=1/(-4*x**2 + sqrt(2)), symbol=x), False), (ArccothRule(a=1, b=-4, c=sqrt(2), context=1/(-4*x**2 + sqrt(2)), symbol=x), x**2 > sqrt(2)/4), (ArctanhRule(a=1, b=-4, c=sqrt(2), context=1/(-4*x**2 + sqrt(2)), symbol=x), x**2 < sqrt(2)/4)], context=1/(-4*x**2 + sqrt(2)), symbol=x)

  1. Añadimos la constante de integración:

    {234acoth⁡(234x)4for x2>24234atanh⁡(234x)4for x2<24+constant\begin{cases} \frac{2^{\frac{3}{4}} \operatorname{acoth}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} > \frac{\sqrt{2}}{4} \\\frac{2^{\frac{3}{4}} \operatorname{atanh}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} < \frac{\sqrt{2}}{4} \end{cases}+ \mathrm{constant}

Respuesta:

{234acoth⁡(234x)4for x2>24234atanh⁡(234x)4for x2<24+constant\begin{cases} \frac{2^{\frac{3}{4}} \operatorname{acoth}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} > \frac{\sqrt{2}}{4} \\\frac{2^{\frac{3}{4}} \operatorname{atanh}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} < \frac{\sqrt{2}}{4} \end{cases}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                         // 3/4      /   3/4\             ___\
  /                      ||2   *acoth\x*2   /       2   \/ 2 |
 |                       ||------------------  for x  > -----|
 |      1                ||        4                      4  |
 | ------------ dx = C + |<                                  |
 |   ___      2          || 3/4      /   3/4\             ___|
 | \/ 2  - 4*x           ||2   *atanh\x*2   /       2   \/ 2 |
 |                       ||------------------  for x  < -----|
/                        \\        4                      4  /
∫1−4x2+2 dx=C+{234acoth⁡(234x)4for x2>24234atanh⁡(234x)4for x2<24\int \frac{1}{- 4 x^{2} + \sqrt{2}}\, dx = C + \begin{cases} \frac{2^{\frac{3}{4}} \operatorname{acoth}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} > \frac{\sqrt{2}}{4} \\\frac{2^{\frac{3}{4}} \operatorname{atanh}{\left(2^{\frac{3}{4}} x \right)}}{4} & \text{for}\: x^{2} < \frac{\sqrt{2}}{4} \end{cases}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-50005000
Trazar el gráfico f(x)
Respuesta [src] 
nan
NaN\text{NaN} 
=
= 
nan
NaN\text{NaN} 
nan
Respuesta numérica [src] 
-0.530158884436561
-0.530158884436561

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

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