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Resolución de integrales/ 1-x^2/ dx/(25(1-x^2))

Integral de dx/(25(1-x^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  4               
  /               
 |                
 |       1        
 |  ----------- dx
 |     /     2\   
 |  25*\1 - x /   
 |                
/                 
3
∫34125(1−x2) dx\int\limits_{3}^{4} \frac{1}{25 \left(1 - x^{2}\right)}\, dx 
Integral(1/(25*(1 - x^2)), (x, 3, 4))
Solución detallada

    PieceweseRule(subfunctions=[(ArctanRule(a=1/25, b=-1, c=1, context=1/(25*(1 - x**2)), symbol=x), False), (ArccothRule(a=1/25, b=-1, c=1, context=1/(25*(1 - x**2)), symbol=x), x**2 > 1), (ArctanhRule(a=1/25, b=-1, c=1, context=1/(25*(1 - x**2)), symbol=x), x**2 < 1)], context=1/(25*(1 - x**2)), symbol=x)

  1. Añadimos la constante de integración:

    {acoth⁡(x)25for x2>1atanh⁡(x)25for x2<1+constant\begin{cases} \frac{\operatorname{acoth}{\left(x \right)}}{25} & \text{for}\: x^{2} > 1 \\\frac{\operatorname{atanh}{\left(x \right)}}{25} & \text{for}\: x^{2} < 1 \end{cases}+ \mathrm{constant}

Respuesta:

{acoth⁡(x)25for x2>1atanh⁡(x)25for x2<1+constant\begin{cases} \frac{\operatorname{acoth}{\left(x \right)}}{25} & \text{for}\: x^{2} > 1 \\\frac{\operatorname{atanh}{\left(x \right)}}{25} & \text{for}\: x^{2} < 1 \end{cases}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                     //acoth(x)       2    \
 |                      ||--------  for x  > 1|
 |      1               ||   25               |
 | ----------- dx = C + |<                    |
 |    /     2\          ||atanh(x)       2    |
 | 25*\1 - x /          ||--------  for x  < 1|
 |                      \\   25               /
/
∫125(1−x2) dx=C+{acoth⁡(x)25for x2>1atanh⁡(x)25for x2<1\int \frac{1}{25 \left(1 - x^{2}\right)}\, dx = C + \begin{cases} \frac{\operatorname{acoth}{\left(x \right)}}{25} & \text{for}\: x^{2} > 1 \\\frac{\operatorname{atanh}{\left(x \right)}}{25} & \text{for}\: x^{2} < 1 \end{cases}
Simplificar
Gráfica
3.004.003.103.203.303.403.503.603.703.803.900.02-0.02
Trazar el gráfico f(x)
Respuesta [src] 
  log(3)   log(4)   log(2)   log(5)
- ------ - ------ + ------ + ------
    50       50       50       50
−log⁡(4)50−log⁡(3)50+log⁡(2)50+log⁡(5)50- \frac{\log{\left(4 \right)}}{50} - \frac{\log{\left(3 \right)}}{50} + \frac{\log{\left(2 \right)}}{50} + \frac{\log{\left(5 \right)}}{50} 
=
= 
  log(3)   log(4)   log(2)   log(5)
- ------ - ------ + ------ + ------
    50       50       50       50
−log⁡(4)50−log⁡(3)50+log⁡(2)50+log⁡(5)50- \frac{\log{\left(4 \right)}}{50} - \frac{\log{\left(3 \right)}}{50} + \frac{\log{\left(2 \right)}}{50} + \frac{\log{\left(5 \right)}}{50} 
-log(3)/50 - log(4)/50 + log(2)/50 + log(5)/50
Respuesta numérica [src] 
-0.00364643113587909
-0.00364643113587909

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

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