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  • Expresiones idénticas

  • (dos *x^ dos +3x)/(dieciséis *x^ cuatro + uno)
  • (2 multiplicar por x al cuadrado más 3x) dividir por (16 multiplicar por x en el grado 4 más 1)
  • (dos multiplicar por x en el grado dos más 3x) dividir por (dieciséis multiplicar por x en el grado cuatro más uno)
  • (2*x2+3x)/(16*x4+1)
  • 2*x2+3x/16*x4+1
  • (2*x²+3x)/(16*x⁴+1)
  • (2*x en el grado 2+3x)/(16*x en el grado 4+1)
  • (2x^2+3x)/(16x^4+1)
  • (2x2+3x)/(16x4+1)
  • 2x2+3x/16x4+1
  • 2x^2+3x/16x^4+1
  • (2*x^2+3x) dividir por (16*x^4+1)
  • (2*x^2+3x)/(16*x^4+1)dx

  • Expresiones semejantes

  • (2*x^2+3x)/(16*x^4-1)
  • (2*x^2-3x)/(16*x^4+1)
Resolución de integrales/ 2*x^2/ 6*x^4/ x^2+3/ (2*x^2+3x)/(16*x^4+1)

Integral de (2*x^2+3x)/(16*x^4+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |     2         
 |  2*x  + 3*x   
 |  ---------- dx
 |      4        
 |  16*x  + 1    
 |               
/                
0
$$\int\limits_{0}^{1} \frac{2 x^{2} + 3 x}{16 x^{4} + 1}\, dx$$ 
Integral((2*x^2 + 3*x)/(16*x^4 + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                            /             ___\                                                                     /             ___\
 |                                      ___    |1    2   x*\/ 2 |                                                              ___    |1    2   x*\/ 2 |
 |    2                      /   2\   \/ 2 *log|- + x  + -------|     ___     /          ___\     ___     /           ___\   \/ 2 *log|- + x  - -------|
 | 2*x  + 3*x          3*atan\4*x /            \4           2   /   \/ 2 *atan\1 + 2*x*\/ 2 /   \/ 2 *atan\-1 + 2*x*\/ 2 /            \4           2   /
 | ---------- dx = C + ------------ - --------------------------- + ------------------------- + -------------------------- + ---------------------------
 |     4                    8                      32                           16                          16                            32            
 | 16*x  + 1                                                                                                                                            
 |                                                                                                                                                      
/
$$\int \frac{2 x^{2} + 3 x}{16 x^{4} + 1}\, dx = C + \frac{\sqrt{2} \log{\left(x^{2} - \frac{\sqrt{2} x}{2} + \frac{1}{4} \right)}}{32} - \frac{\sqrt{2} \log{\left(x^{2} + \frac{\sqrt{2} x}{2} + \frac{1}{4} \right)}}{32} + \frac{3 \operatorname{atan}{\left(4 x^{2} \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(2 \sqrt{2} x - 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(2 \sqrt{2} x + 1 \right)}}{16}$$
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Gráfica
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Respuesta [src] 
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         /          ______________      /                                                                                                                                                                                                                                                                                                                                               ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                                                                                                                                                                 ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                                                                                                                                                               ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                       ______________                                                                                                                                                                                                                                                                    ______________                                                      \     ___    |31067    9765*\/ 2    12613*\/  19 - 6*\/ 2     1221*\/ 2 *\/  19 - 6*\/ 2  |     ___    |115047   9119*\/ 2    57155*\/  19 + 6*\/ 2     717*\/ 2 *\/  19 + 6*\/ 2  |     ___    |31067    12613*\/  19 + 6*\/ 2     9765*\/ 2    1221*\/ 2 *\/  19 + 6*\/ 2  |     ___    |115047   57155*\/  19 - 6*\/ 2     9119*\/ 2    717*\/ 2 *\/  19 - 6*\/ 2  |
        /          /          ___       |                                                                                                                                                                                                           ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                             ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                           ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                      /          ___                                                                                                                               ___                                                                                                                            ___   /          ___                                                       |   \/ 2 *log|------ - ---------- + ----------------------- - ----------------------------|   \/ 2 *log|------ + ---------- + ----------------------- + ---------------------------|   \/ 2 *log|------ - ----------------------- + ---------- - ----------------------------|   \/ 2 *log|------ - ----------------------- - ---------- + ---------------------------|
       /    21   \/  19 + 6*\/ 2        |                                                                 1166                                                                                                                                  4*\/ 2                                                                                                                           108*\/  19 + 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 + 6*\/ 2                                                        |        /    21   \/  19 + 6*\/ 2        |                                                                   126                                                                                                                                   4*\/ 2                                                                                                                           108*\/  19 + 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 + 6*\/ 2                                                        |        /    21   \/  19 - 6*\/ 2        |                                                                 126                                                                                                                                   4*\/ 2                                                                                                                           108*\/  19 - 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 - 6*\/ 2                                                        |        /    21   \/  19 - 6*\/ 2        |                                                                 1166                                                                                                                           108*\/  19 - 6*\/ 2                                                                                                                            4*\/ 2                                                                                                                         3*\/ 2 *\/  19 - 6*\/ 2                                                        |            \104329     104329              417316                      417316           /            \104329     104329              417316                      417316          /            \104329            417316             104329                417316           /            \104329            417316             104329                417316          /
- 2*  /    --- - ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- - ----------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------
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                                        \108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2   /                                         \  108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2   /                                         \108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2   /                                         \108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2   /
$$- 2 \sqrt{\frac{21}{512} - \frac{\sqrt{6 \sqrt{2} + 19}}{256}} \operatorname{atan}{\left(- \frac{4 \sqrt{2}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{3 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{108 \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{1166}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} \right)} + \frac{\sqrt{2} \log{\left(- \frac{12613 \sqrt{6 \sqrt{2} + 19}}{417316} - \frac{1221 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{9765 \sqrt{2}}{104329} + \frac{31067}{104329} \right)}}{32} - \frac{\sqrt{2} \log{\left(\frac{717 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{9119 \sqrt{2}}{104329} + \frac{57155 \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{115047}{104329} \right)}}{32} + \frac{\sqrt{2} \log{\left(- \frac{57155 \sqrt{19 - 6 \sqrt{2}}}{417316} - \frac{9119 \sqrt{2}}{104329} + \frac{717 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{115047}{104329} \right)}}{32} - \frac{\sqrt{2} \log{\left(- \frac{9765 \sqrt{2}}{104329} - \frac{1221 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{12613 \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{31067}{104329} \right)}}{32} + 2 \sqrt{\frac{21}{512} - \frac{\sqrt{6 \sqrt{2} + 19}}{256}} \operatorname{atan}{\left(- \frac{126}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} - \frac{4 \sqrt{2}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{3 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{108 \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} \right)} + 2 \sqrt{\frac{\sqrt{19 - 6 \sqrt{2}}}{256} + \frac{21}{512}} \operatorname{atan}{\left(- \frac{3 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} - \frac{4 \sqrt{2}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{126}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{108 \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} \right)} + 2 \sqrt{\frac{\sqrt{19 - 6 \sqrt{2}}}{256} + \frac{21}{512}} \operatorname{atan}{\left(- \frac{108 \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{4 \sqrt{2}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{3 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{1166}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} \right)}$$ 
=
= 
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          _________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               _________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 _________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               _________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                ___           /          ___           ___   /          ___ |            |                ___           /          ___          ___   /          ___ |            |                 /          ___           ___          ___   /          ___ |            |                 /          ___           ___         ___   /          ___ |
         /          ______________      /                                                                                                                                                                                                                                                                                                                                               ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                                                                                                                                                                 ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                                                                                                                                                               ______________                                                                                                                            ______________                                                      \          /          ______________      /                                                                                                                                                                                                       ______________                                                                                                                                                                                                                                                                    ______________                                                      \     ___    |31067    9765*\/ 2    12613*\/  19 - 6*\/ 2     1221*\/ 2 *\/  19 - 6*\/ 2  |     ___    |115047   9119*\/ 2    57155*\/  19 + 6*\/ 2     717*\/ 2 *\/  19 + 6*\/ 2  |     ___    |31067    12613*\/  19 + 6*\/ 2     9765*\/ 2    1221*\/ 2 *\/  19 + 6*\/ 2  |     ___    |115047   57155*\/  19 - 6*\/ 2     9119*\/ 2    717*\/ 2 *\/  19 - 6*\/ 2  |
        /          /          ___       |                                                                                                                                                                                                           ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                             ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                           ___                                                                                                                                /          ___                                                                                                                      ___   /          ___                                                       |         /          /          ___       |                                                                                                                                                                                                      /          ___                                                                                                                               ___                                                                                                                            ___   /          ___                                                       |   \/ 2 *log|------ - ---------- + ----------------------- - ----------------------------|   \/ 2 *log|------ + ---------- + ----------------------- + ---------------------------|   \/ 2 *log|------ - ----------------------- + ---------- - ----------------------------|   \/ 2 *log|------ - ----------------------- - ---------- + ---------------------------|
       /    21   \/  19 + 6*\/ 2        |                                                                 1166                                                                                                                                  4*\/ 2                                                                                                                           108*\/  19 + 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 + 6*\/ 2                                                        |        /    21   \/  19 + 6*\/ 2        |                                                                   126                                                                                                                                   4*\/ 2                                                                                                                           108*\/  19 + 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 + 6*\/ 2                                                        |        /    21   \/  19 - 6*\/ 2        |                                                                 126                                                                                                                                   4*\/ 2                                                                                                                           108*\/  19 - 6*\/ 2                                                                                                                   3*\/ 2 *\/  19 - 6*\/ 2                                                        |        /    21   \/  19 - 6*\/ 2        |                                                                 1166                                                                                                                           108*\/  19 - 6*\/ 2                                                                                                                            4*\/ 2                                                                                                                         3*\/ 2 *\/  19 - 6*\/ 2                                                        |            \104329     104329              417316                      417316           /            \104329     104329              417316                      417316          /            \104329            417316             104329                417316           /            \104329            417316             104329                417316          /
- 2*  /    --- - ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- - ----------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------| + 2*  /    --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------
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                                        \108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2   /                                         \  108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2      108*\/   21 - 2*\/  19 + 6*\/ 2    + 18*\/ 2 *\/   21 - 2*\/  19 + 6*\/ 2    + \/ 2 *\/  19 + 6*\/ 2  *\/   21 - 2*\/  19 + 6*\/ 2   /                                         \108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2   /                                         \108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2      108*\/   21 + 2*\/  19 - 6*\/ 2    - 18*\/ 2 *\/   21 + 2*\/  19 - 6*\/ 2    + \/ 2 *\/  19 - 6*\/ 2  *\/   21 + 2*\/  19 - 6*\/ 2   /
$$- 2 \sqrt{\frac{21}{512} - \frac{\sqrt{6 \sqrt{2} + 19}}{256}} \operatorname{atan}{\left(- \frac{4 \sqrt{2}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{3 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{108 \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{1166}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} \right)} + \frac{\sqrt{2} \log{\left(- \frac{12613 \sqrt{6 \sqrt{2} + 19}}{417316} - \frac{1221 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{9765 \sqrt{2}}{104329} + \frac{31067}{104329} \right)}}{32} - \frac{\sqrt{2} \log{\left(\frac{717 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{9119 \sqrt{2}}{104329} + \frac{57155 \sqrt{6 \sqrt{2} + 19}}{417316} + \frac{115047}{104329} \right)}}{32} + \frac{\sqrt{2} \log{\left(- \frac{57155 \sqrt{19 - 6 \sqrt{2}}}{417316} - \frac{9119 \sqrt{2}}{104329} + \frac{717 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{115047}{104329} \right)}}{32} - \frac{\sqrt{2} \log{\left(- \frac{9765 \sqrt{2}}{104329} - \frac{1221 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{12613 \sqrt{19 - 6 \sqrt{2}}}{417316} + \frac{31067}{104329} \right)}}{32} + 2 \sqrt{\frac{21}{512} - \frac{\sqrt{6 \sqrt{2} + 19}}{256}} \operatorname{atan}{\left(- \frac{126}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} - \frac{4 \sqrt{2}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{3 \sqrt{2} \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} + \frac{108 \sqrt{6 \sqrt{2} + 19}}{\sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} \sqrt{6 \sqrt{2} + 19} + 18 \sqrt{2} \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}} + 108 \sqrt{21 - 2 \sqrt{6 \sqrt{2} + 19}}} \right)} + 2 \sqrt{\frac{\sqrt{19 - 6 \sqrt{2}}}{256} + \frac{21}{512}} \operatorname{atan}{\left(- \frac{3 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} - \frac{4 \sqrt{2}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{126}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{108 \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} \right)} + 2 \sqrt{\frac{\sqrt{19 - 6 \sqrt{2}}}{256} + \frac{21}{512}} \operatorname{atan}{\left(- \frac{108 \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{4 \sqrt{2}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{3 \sqrt{2} \sqrt{19 - 6 \sqrt{2}}}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} + \frac{1166}{- 18 \sqrt{2} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + \sqrt{2} \sqrt{19 - 6 \sqrt{2}} \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21} + 108 \sqrt{2 \sqrt{19 - 6 \sqrt{2}} + 21}} \right)}$$ 
-2*sqrt(21/512 - sqrt(19 + 6*sqrt(2))/256)*atan(1166/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 108*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))))) + 2*sqrt(21/512 - sqrt(19 + 6*sqrt(2))/256)*atan(-126/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 108*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))))) + 2*sqrt(21/512 + sqrt(19 - 6*sqrt(2))/256)*atan(126/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 108*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 3*sqrt(2)*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))))) + 2*sqrt(21/512 + sqrt(19 - 6*sqrt(2))/256)*atan(1166/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 108*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 4*sqrt(2)/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))))) - sqrt(2)*log(31067/104329 - 9765*sqrt(2)/104329 + 12613*sqrt(19 - 6*sqrt(2))/417316 - 1221*sqrt(2)*sqrt(19 - 6*sqrt(2))/417316)/32 - sqrt(2)*log(115047/104329 + 9119*sqrt(2)/104329 + 57155*sqrt(19 + 6*sqrt(2))/417316 + 717*sqrt(2)*sqrt(19 + 6*sqrt(2))/417316)/32 + sqrt(2)*log(31067/104329 - 12613*sqrt(19 + 6*sqrt(2))/417316 + 9765*sqrt(2)/104329 - 1221*sqrt(2)*sqrt(19 + 6*sqrt(2))/417316)/32 + sqrt(2)*log(115047/104329 - 57155*sqrt(19 - 6*sqrt(2))/417316 - 9119*sqrt(2)/104329 + 717*sqrt(2)*sqrt(19 - 6*sqrt(2))/417316)/32
Respuesta numérica [src] 
0.651372294741051
0.651372294741051

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

    © Sr Examen – Калькулятор