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Resolución de integrales/ 9+x^2/ dx/(sqrt9+x^2)

Integral de dx/(sqrt9+x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |   29    2   
 |  t   + x    
 |             
/              
0
∫011t29+x2 dx\int\limits_{0}^{1} \frac{1}{t^{29} + x^{2}}\, dx 
Integral(1/(t^29 + x^2), (x, 0, 1))
Solución detallada

  1. Integral 1x2+1\frac{1}{x^{2} + 1} es atan⁡(xt29)t29\frac{\operatorname{atan}{\left(\frac{x}{\sqrt{t^{29}}} \right)}}{\sqrt{t^{29}}}.

  2. Añadimos la constante de integración:

    atan⁡(xt29)t29+constant\frac{\operatorname{atan}{\left(\frac{x}{\sqrt{t^{29}}} \right)}}{\sqrt{t^{29}}}+ \mathrm{constant}

Respuesta:

atan⁡(xt29)t29+constant\frac{\operatorname{atan}{\left(\frac{x}{\sqrt{t^{29}}} \right)}}{\sqrt{t^{29}}}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                         /   x    \
                     atan|--------|
  /                      |   _____|
 |                       |  /  29 |
 |    1                  \\/  t   /
 | -------- dx = C + --------------
 |  29    2                _____   
 | t   + x                /  29    
 |                      \/  t      
/
∫1t29+x2 dx=C+atan⁡(xt29)t29\int \frac{1}{t^{29} + x^{2}}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{t^{29}}} \right)}}{\sqrt{t^{29}}}
Simplificar
Respuesta [src] 
     _____    /          _____\        _____    /             _____\        _____    /         _____\        _____    /             _____\
    / -1      |  29     / -1  |       / -1      |     29     / -1  |       / -1      | 29     / -1  |       / -1      |     29     / -1  |
   /  --- *log|-t  *   /  --- |      /  --- *log|1 + t  *   /  --- |      /  --- *log|t  *   /  --- |      /  --- *log|1 - t  *   /  --- |
  /    29     |       /    29 |     /    29     |          /    29 |     /    29     |      /    29 |     /    29     |          /    29 |
\/    t       \     \/    t   /   \/    t       \        \/    t   /   \/    t       \    \/    t   /   \/    t       \        \/    t   /
------------------------------- + ---------------------------------- - ------------------------------ - ----------------------------------
               2                                  2                                  2                                  2
−1t29log⁡(−t29−1t29)2−−1t29log⁡(t29−1t29)2−−1t29log⁡(−t29−1t29+1)2+−1t29log⁡(t29−1t29+1)2\frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} + \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} 
=
= 
     _____    /          _____\        _____    /             _____\        _____    /         _____\        _____    /             _____\
    / -1      |  29     / -1  |       / -1      |     29     / -1  |       / -1      | 29     / -1  |       / -1      |     29     / -1  |
   /  --- *log|-t  *   /  --- |      /  --- *log|1 + t  *   /  --- |      /  --- *log|t  *   /  --- |      /  --- *log|1 - t  *   /  --- |
  /    29     |       /    29 |     /    29     |          /    29 |     /    29     |      /    29 |     /    29     |          /    29 |
\/    t       \     \/    t   /   \/    t       \        \/    t   /   \/    t       \    \/    t   /   \/    t       \        \/    t   /
------------------------------- + ---------------------------------- - ------------------------------ - ----------------------------------
               2                                  2                                  2                                  2
−1t29log⁡(−t29−1t29)2−−1t29log⁡(t29−1t29)2−−1t29log⁡(−t29−1t29+1)2+−1t29log⁡(t29−1t29+1)2\frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} + \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} 
sqrt(-1/t^29)*log(-t^29*sqrt(-1/t^29))/2 + sqrt(-1/t^29)*log(1 + t^29*sqrt(-1/t^29))/2 - sqrt(-1/t^29)*log(t^29*sqrt(-1/t^29))/2 - sqrt(-1/t^29)*log(1 - t^29*sqrt(-1/t^29))/2

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

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