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Resolución de integrales/ (-1)/((2*sqrt(2))*cos(x)+3)

Integral de (-1)/((2sqrt(2))cos(x)+3) dx

Solución

Ha introducido [src]

  1                      
  /                      
 |                       
 |         -1            
 |  ------------------ dx
 |      ___              
 |  2*\/ 2 *cos(x) + 3   
 |                       
/                        
0

$$\int\limits_{0}^{1} \left(- \frac{1}{2 \sqrt{2} \cos{\left(x \right)} + 3}\right)\, dx$$

Integral(-1/((2*sqrt(2))*cos(x) + 3), (x, 0, 1))

Solución detallada

La integral del producto de una función por una constante es la constante por la integral de esta función:

$\int \left(- \frac{1}{2 \sqrt{2} \cos{\left(x \right)} + 3}\right)\, dx = - \int \frac{1}{2 \sqrt{2} \cos{\left(x \right)} + 3}\, dx$
1. No puedo encontrar los pasos en la búsqueda de esta integral.
  
  Pero la integral
  
  $\frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}}$
Por lo tanto, el resultado es: $\frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}}$
Ahora simplificar:

$\frac{i \left(- 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} + 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} - 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)} + 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)}\right)}{\left(7942546277405390632803 - 5616228332641321147898 \sqrt{2}\right) \sqrt{12 \sqrt{2} + 17}}$
Añadimos la constante de integración:

$\frac{i \left(- 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} + 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} - 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)} + 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)}\right)}{\left(7942546277405390632803 - 5616228332641321147898 \sqrt{2}\right) \sqrt{12 \sqrt{2} + 17}}+ \mathrm{constant}$

Respuesta:

$\frac{i \left(- 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} + 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{-17 - 12 \sqrt{2}} \right)} - 1362725501650887306817 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)} + 963592443113182178088 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{-17 - 12 \sqrt{2}} \right)}\right)}{\left(7942546277405390632803 - 5616228332641321147898 \sqrt{2}\right) \sqrt{12 \sqrt{2} + 17}}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

                                                                           /       _______________         \                                                                /     _______________         \                                                                    /     _______________         \                                                                /       _______________         \             
  /                                                                        |      /           ___       /x\|                                                                |    /           ___       /x\|                                                             ___    |    /           ___       /x\|                                                         ___    |      /           ___       /x\|             
 |                                             1362725501650887306817*I*log|- I*\/  17 + 12*\/ 2   + tan|-||                                    1362725501650887306817*I*log|I*\/  17 + 12*\/ 2   + tan|-||                                   963592443113182178088*I*\/ 2 *log|I*\/  17 + 12*\/ 2   + tan|-||                               963592443113182178088*I*\/ 2 *log|- I*\/  17 + 12*\/ 2   + tan|-||             
 |        -1                                                               \                            \2//                                                                \                          \2//                                                                    \                          \2//                                                                \                            \2//             
 | ------------------ dx = C - --------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------
 |     ___                                                 _______________                                   _______________                               _______________                                   _______________                               _______________                                   _______________                               _______________                                   _______________
 | 2*\/ 2 *cos(x) + 3                                     /           ___                             ___   /           ___                               /           ___                             ___   /           ___                               /           ___                             ___   /           ___                               /           ___                             ___   /           ___ 
 |                             - 7942546277405390632803*\/  17 + 12*\/ 2   + 5616228332641321147898*\/ 2 *\/  17 + 12*\/ 2     - 7942546277405390632803*\/  17 + 12*\/ 2   + 5616228332641321147898*\/ 2 *\/  17 + 12*\/ 2     - 7942546277405390632803*\/  17 + 12*\/ 2   + 5616228332641321147898*\/ 2 *\/  17 + 12*\/ 2     - 7942546277405390632803*\/  17 + 12*\/ 2   + 5616228332641321147898*\/ 2 *\/  17 + 12*\/ 2  
/

$$\int \left(- \frac{1}{2 \sqrt{2} \cos{\left(x \right)} + 3}\right)\, dx = C + \frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{1362725501650887306817 i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{963592443113182178088 \sqrt{2} i \log{\left(\tan{\left(\frac{x}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 7942546277405390632803 \sqrt{12 \sqrt{2} + 17} + 5616228332641321147898 \sqrt{2} \sqrt{12 \sqrt{2} + 17}}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

                                         /          /   _______________\\                                                                                                                                                   /            /   _______________\\                                                                                                                                                    /            /   _______________\\                                                                                                                                                   /          /   _______________\\                                                                                                        
                                         |pi*I      |  /           ___ ||                                                          /       _______________           \                                                      |  pi*I      |  /           ___ ||                                                          /     _______________           \                                                     ___ |  pi*I      |  /           ___ ||                                                          /     _______________           \                                                    ___ |pi*I      |  /           ___ ||                                                          /       _______________           \           
                   1180872205318713601*I*|---- + log\\/  17 + 12*\/ 2  /|                                                          |      /           ___            |                                1180872205318713601*I*|- ---- + log\\/  17 + 12*\/ 2  /|                                                          |    /           ___            |                              835002744095575440*I*\/ 2 *|- ---- + log\\/  17 + 12*\/ 2  /|                                                   ___    |    /           ___            |                             835002744095575440*I*\/ 2 *|---- + log\\/  17 + 12*\/ 2  /|                                                   ___    |      /           ___            |           
                                         \ 2                            /                                 1180872205318713601*I*log\- I*\/  17 + 12*\/ 2   + tan(1/2)/                                                      \   2                            /                                 1180872205318713601*I*log\I*\/  17 + 12*\/ 2   + tan(1/2)/                                                         \   2                            /                            835002744095575440*I*\/ 2 *log\I*\/  17 + 12*\/ 2   + tan(1/2)/                                                        \ 2                            /                            835002744095575440*I*\/ 2 *log\- I*\/  17 + 12*\/ 2   + tan(1/2)/           
- --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------
                           _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________
                          /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___ 
  - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2

$$\frac{835002744095575440 \sqrt{2} i \log{\left(\tan{\left(\frac{1}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{1180872205318713601 i \log{\left(\tan{\left(\frac{1}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{1180872205318713601 i \left(\log{\left(\sqrt{12 \sqrt{2} + 17} \right)} - \frac{i \pi}{2}\right)}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} + \frac{835002744095575440 \sqrt{2} i \left(\log{\left(\sqrt{12 \sqrt{2} + 17} \right)} + \frac{i \pi}{2}\right)}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{1180872205318713601 i \left(\log{\left(\sqrt{12 \sqrt{2} + 17} \right)} + \frac{i \pi}{2}\right)}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{835002744095575440 \sqrt{2} i \left(\log{\left(\sqrt{12 \sqrt{2} + 17} \right)} - \frac{i \pi}{2}\right)}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{835002744095575440 \sqrt{2} i \log{\left(\tan{\left(\frac{1}{2} \right)} + i \sqrt{12 \sqrt{2} + 17} \right)}}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}} - \frac{1180872205318713601 i \log{\left(\tan{\left(\frac{1}{2} \right)} - i \sqrt{12 \sqrt{2} + 17} \right)}}{- 6882627592338442563 \sqrt{12 \sqrt{2} + 17} + 4866752642924153522 \sqrt{2} \sqrt{12 \sqrt{2} + 17}}$$

                                         /          /   _______________\\                                                                                                                                                   /            /   _______________\\                                                                                                                                                    /            /   _______________\\                                                                                                                                                   /          /   _______________\\                                                                                                        
                                         |pi*I      |  /           ___ ||                                                          /       _______________           \                                                      |  pi*I      |  /           ___ ||                                                          /     _______________           \                                                     ___ |  pi*I      |  /           ___ ||                                                          /     _______________           \                                                    ___ |pi*I      |  /           ___ ||                                                          /       _______________           \           
                   1180872205318713601*I*|---- + log\\/  17 + 12*\/ 2  /|                                                          |      /           ___            |                                1180872205318713601*I*|- ---- + log\\/  17 + 12*\/ 2  /|                                                          |    /           ___            |                              835002744095575440*I*\/ 2 *|- ---- + log\\/  17 + 12*\/ 2  /|                                                   ___    |    /           ___            |                             835002744095575440*I*\/ 2 *|---- + log\\/  17 + 12*\/ 2  /|                                                   ___    |      /           ___            |           
                                         \ 2                            /                                 1180872205318713601*I*log\- I*\/  17 + 12*\/ 2   + tan(1/2)/                                                      \   2                            /                                 1180872205318713601*I*log\I*\/  17 + 12*\/ 2   + tan(1/2)/                                                         \   2                            /                            835002744095575440*I*\/ 2 *log\I*\/  17 + 12*\/ 2   + tan(1/2)/                                                        \ 2                            /                            835002744095575440*I*\/ 2 *log\- I*\/  17 + 12*\/ 2   + tan(1/2)/           
- --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------
                           _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________                            _______________                                _______________
                          /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___                            /           ___                          ___   /           ___ 
  - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2     - 6882627592338442563*\/  17 + 12*\/ 2   + 4866752642924153522*\/ 2 *\/  17 + 12*\/ 2

-1180872205318713601*i*(pi*i/2 + log(sqrt(17 + 12*sqrt(2))))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) - 1180872205318713601*i*log(-i*sqrt(17 + 12*sqrt(2)) + tan(1/2))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) + 1180872205318713601*i*(-pi*i/2 + log(sqrt(17 + 12*sqrt(2))))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) + 1180872205318713601*i*log(i*sqrt(17 + 12*sqrt(2)) + tan(1/2))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) - 835002744095575440*i*sqrt(2)*(-pi*i/2 + log(sqrt(17 + 12*sqrt(2))))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) - 835002744095575440*i*sqrt(2)*log(i*sqrt(17 + 12*sqrt(2)) + tan(1/2))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) + 835002744095575440*i*sqrt(2)*(pi*i/2 + log(sqrt(17 + 12*sqrt(2))))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2))) + 835002744095575440*i*sqrt(2)*log(-i*sqrt(17 + 12*sqrt(2)) + tan(1/2))/(-6882627592338442563*sqrt(17 + 12*sqrt(2)) + 4866752642924153522*sqrt(2)*sqrt(17 + 12*sqrt(2)))

Respuesta numérica [src]

-0.186915276624842

-0.186915276624842

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

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Expresiones con funciones

Integral de (-1)/((2sqrt(2))cos(x)+3) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Integral de (-1)/((2*sqrt(2))*cos(x)+3) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución

Integral de (-1)/((2sqrt(2))cos(x)+3) dx