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Expresiones idénticas
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uno dividir por (tres más dos multiplicar por x en el grado dos más cinco multiplicar por x en el grado cuatro)
1/(3+2*x2+5*x4)
1/3+2*x2+5*x4
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1/3+2x^2+5x^4
1 dividir por (3+2*x^2+5*x^4)
1/(3+2*x^2+5*x^4)dx
Expresiones semejantes
1/(3+2*x^2-5*x^4)
1/(3-2*x^2+5*x^4)

Resolución de integrales/ 5*x^4/ x^2+5/ 2*x^2/ 1/(3+2*x^2+5*x^4)

Integral de 1/(3+2x^2+5x^4) dx

Solución

Ha introducido [src]

 oo                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |         2      4   
 |  3 + 2*x  + 5*x    
 |                    
/                     
1

$$\int\limits_{1}^{\infty} \frac{1}{5 x^{4} + \left(2 x^{2} + 3\right)}\, dx$$

Integral(1/(3 + 2*x^2 + 5*x^4), (x, 1, oo))

Respuesta (Indefinida) [src]

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    _______________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             _______________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
  /                              _______________    /                            /              ____________               ____________             ____________    ____________\               ____________                ____________\        _______________    /                            /              ____________               ____________             ____________    ____________\               ____________                ____________\          /                          ____________      /                                                         ____________                                                                                                              ____________                                                                                                                                                                                                                         ____________    ____________                                       \          /                          ____________      /                                                       ____________                                                                                                              ____________                                                                                                                                                                                                                         ____________    ____________                                       \
 |                              /          ____     |                   ____     |      ____   /       ____        ____   /       ____      ____   /       ____    /       ____ |        ___   /       ____         ____   /       ____ |       /          ____     |                   ____     |      ____   /       ____        ____   /       ____      ____   /       ____    /       ____ |        ___   /       ____         ____   /       ____ |         /           ____     ___   /       ____       |                                                        /       ____                                                                                                       ____   /       ____                                                                                                             ____                                                                                                  ___   /       ____    /       ____                                        |         /           ____     ___   /       ____       |                                                      /       ____                                                                                                       ____   /       ____                                                                                                             ____                                                                                                  ___   /       ____    /       ____                                        |
 |        1                    /   1     \/ 15      |  103    2   244*\/ 15      |  4*\/ 35 *\/  1 + \/ 15     4*\/ 21 *\/  1 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |   57*\/ 2 *\/  8 + \/ 15     32*\/ 30 *\/  8 + \/ 15  |      /   1     \/ 15      |  103    2   244*\/ 15      |  4*\/ 21 *\/  1 + \/ 15     4*\/ 35 *\/  1 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |   57*\/ 2 *\/  8 + \/ 15     32*\/ 30 *\/  8 + \/ 15  |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                   12*\/  1 + \/ 15                                                                                                    4*\/ 15 *\/  1 + \/ 15                                                                                                       10*x*\/ 21                                                                                               3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                 12*\/  1 + \/ 15                                                                                                    4*\/ 15 *\/  1 + \/ 15                                                                                                       10*x*\/ 21                                                                                               3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |
 | --------------- dx = C +   /   ---- + ------ *log|- --- + x  + ---------- + x*|- ------------------------ + ------------------------ + --------------------------------------| - ------------------------ + -------------------------| -   /   ---- + ------ *log|- --- + x  + ---------- + x*|- ------------------------ + ------------------------ - --------------------------------------| - ------------------------ + -------------------------| + 2*  /    ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| + 2*  /    ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------|
 |        2      4          \/    1344    1344      \  175           525         \             35                         35                                35                  /             175                         525           /   \/    1344    1344      \  175           525         \             35                         35                                35                  /             175                         525           /     \/     1344    448              672               |         ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|     \/     1344    448              672               |       ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|
 | 3 + 2*x  + 5*x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |        /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________ |                                                       |      /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________          /                           ____________             ____________    /                           ____________ |
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |       /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____  |                                                       |     /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____  |
/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \  14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /                                                       \14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /

$$\int \frac{1}{5 x^{4} + \left(2 x^{2} + 3\right)}\, dx = C + \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(x^{2} + x \left(- \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35}\right) - \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{103}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{244 \sqrt{15}}{525} \right)} - \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(x^{2} + x \left(- \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} - \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35}\right) - \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{103}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{244 \sqrt{15}}{525} \right)} + 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(\frac{10 \sqrt{21} x}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} + 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(\frac{10 \sqrt{21} x}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

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     _______________    /                               ____________               ____________               ____________                ____________             ____________    ____________\        _______________    /                               ____________               ____________               ____________                ____________             ____________    ____________\          /                          ____________      /                                                         ____________                                                                                                                                                                                                                                     ____________                                                                                                  ____________    ____________                                       \          /                          ____________      /                                                                                                                                                                              ____________                                                                                                              ____________                                                                                                  ____________    ____________                                       \                /                           ____________ 
    /          ____     |            ____        ___   /       ____        ____   /       ____        ____   /       ____         ____   /       ____      ____   /       ____    /       ____ |       /          ____     |            ____        ___   /       ____        ____   /       ____        ____   /       ____         ____   /       ____      ____   /       ____    /       ____ |         /           ____     ___   /       ____       |                                                        /       ____                                                                                                               ____                                                                                                           ____   /       ____                                                                                            ___   /       ____    /       ____                                        |         /           ____     ___   /       ____       |                                                          ____                                                                                                               /       ____                                                                                                       ____   /       ____                                                                                            ___   /       ____    /       ____                                        |        ____   /          ____       ___   /       ____  
   /   1     \/ 15      | 72   244*\/ 15    57*\/ 2 *\/  8 + \/ 15     4*\/ 21 *\/  1 + \/ 15     4*\/ 35 *\/  1 + \/ 15     32*\/ 30 *\/  8 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |      /   1     \/ 15      | 72   244*\/ 15    57*\/ 2 *\/  8 + \/ 15     4*\/ 35 *\/  1 + \/ 15     4*\/ 21 *\/  1 + \/ 15     32*\/ 30 *\/  8 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                   12*\/  1 + \/ 15                                                                                                           10*\/ 21                                                                                                        4*\/ 15 *\/  1 + \/ 15                                                                                         3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                     10*\/ 21                                                                                                           12*\/  1 + \/ 15                                                                                                    4*\/ 15 *\/  1 + \/ 15                                                                                         3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |   pi*\/ 21 *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   
  /   ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- - --------------------------------------| -   /   ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- + --------------------------------------| - 2*  /    ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| - 2*  /    ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------
\/    1344    1344      \175      525                 175                         35                         35                         525                                35                  /   \/    1344    1344      \175      525                 175                         35                         35                         525                                35                  /     \/     1344    448              672               |         ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|     \/     1344    448              672               |       ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|                             84                          
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                                                                                                                                                                                                                                                                                                                                                                                                                                                          |       /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____  |                                                       |     /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____          /          ____       ___   /       ____       ___   /       ____    /          ____       ___   /       ____  |                                                         
                                                                                                                                                                                                                                                                                                                                                                                                                                                          \  14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /                                                       \14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /

$$- 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} - \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} + \frac{244 \sqrt{15}}{525} \right)} - 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} + \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} - \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{244 \sqrt{15}}{525} \right)} + \frac{\sqrt{21} \pi \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}}{84}$$

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     _______________    /                               ____________               ____________               ____________                ____________             ____________    ____________\        _______________    /                               ____________               ____________               ____________                ____________             ____________    ____________\          /                          ____________      /                                                         ____________                                                                                                                                                                                                                                     ____________                                                                                                  ____________    ____________                                       \          /                          ____________      /                                                                                                                                                                              ____________                                                                                                              ____________                                                                                                  ____________    ____________                                       \                /                           ____________ 
    /          ____     |            ____        ___   /       ____        ____   /       ____        ____   /       ____         ____   /       ____      ____   /       ____    /       ____ |       /          ____     |            ____        ___   /       ____        ____   /       ____        ____   /       ____         ____   /       ____      ____   /       ____    /       ____ |         /           ____     ___   /       ____       |                                                        /       ____                                                                                                               ____                                                                                                           ____   /       ____                                                                                            ___   /       ____    /       ____                                        |         /           ____     ___   /       ____       |                                                          ____                                                                                                               /       ____                                                                                                       ____   /       ____                                                                                            ___   /       ____    /       ____                                        |        ____   /          ____       ___   /       ____  
   /   1     \/ 15      | 72   244*\/ 15    57*\/ 2 *\/  8 + \/ 15     4*\/ 21 *\/  1 + \/ 15     4*\/ 35 *\/  1 + \/ 15     32*\/ 30 *\/  8 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |      /   1     \/ 15      | 72   244*\/ 15    57*\/ 2 *\/  8 + \/ 15     4*\/ 35 *\/  1 + \/ 15     4*\/ 21 *\/  1 + \/ 15     32*\/ 30 *\/  8 + \/ 15     \/ 42 *\/  1 + \/ 15  *\/  8 + \/ 15  |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                   12*\/  1 + \/ 15                                                                                                           10*\/ 21                                                                                                        4*\/ 15 *\/  1 + \/ 15                                                                                         3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |        /    1     \/ 15    \/ 2 *\/  8 + \/ 15        |                                                     10*\/ 21                                                                                                           12*\/  1 + \/ 15                                                                                                    4*\/ 15 *\/  1 + \/ 15                                                                                         3*\/ 2 *\/  1 + \/ 15  *\/  8 + \/ 15                                         |   pi*\/ 21 *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   
  /   ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- - --------------------------------------| -   /   ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- + --------------------------------------| - 2*  /    ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| - 2*  /    ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------
\/    1344    1344      \175      525                 175                         35                         35                         525                                35                  /   \/    1344    1344      \175      525                 175                         35                         35                         525                                35                  /     \/     1344    448              672               |         ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|     \/     1344    448              672               |       ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________          ________________________________________                             ________________________________________|                             84                          
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                                                                                                                                                                                                                                                                                                                                                                                                                                                          \  14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /                                                       \14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15      14*\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15    + \/ 2 *\/  8 + \/ 15  *\/   1 + 3*\/ 15  - 2*\/ 2 *\/  8 + \/ 15   /

sqrt(1/1344 + sqrt(15)/1344)*log(72/175 + 244*sqrt(15)/525 - 57*sqrt(2)*sqrt(8 + sqrt(15))/175 - 4*sqrt(21)*sqrt(1 + sqrt(15))/35 + 4*sqrt(35)*sqrt(1 + sqrt(15))/35 + 32*sqrt(30)*sqrt(8 + sqrt(15))/525 - sqrt(42)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/35) - sqrt(1/1344 + sqrt(15)/1344)*log(72/175 + 244*sqrt(15)/525 - 57*sqrt(2)*sqrt(8 + sqrt(15))/175 - 4*sqrt(35)*sqrt(1 + sqrt(15))/35 + 4*sqrt(21)*sqrt(1 + sqrt(15))/35 + 32*sqrt(30)*sqrt(8 + sqrt(15))/525 + sqrt(42)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/35) - 2*sqrt(1/1344 + sqrt(15)/448 - sqrt(2)*sqrt(8 + sqrt(15))/672)*atan(-12*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 10*sqrt(21)/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 4*sqrt(15)*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) - 3*sqrt(2)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))))) - 2*sqrt(1/1344 + sqrt(15)/448 - sqrt(2)*sqrt(8 + sqrt(15))/672)*atan(10*sqrt(21)/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 12*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) - 4*sqrt(15)*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 3*sqrt(2)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))))) + pi*sqrt(21)*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))/84

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

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Integral de 1/(3+2x^2+5x^4) dx

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Gráfico:

Definida a trozos:

Solución

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Integral de 1/(3+2*x^2+5*x^4) dx

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Solución

Integral de 1/(3+2x^2+5x^4) dx