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Resolución de integrales/ sqrt(1+(sqrt(6(x-1))^3)/(2(x-1)))

Integral de sqrt(1+(sqrt(6(x-1))^3)/(2(x-1))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                              
  /                              
 |                               
 |        ____________________   
 |       /                  3    
 |      /        ___________     
 |     /       \/ 6*(x - 1)      
 |    /    1 + --------------  dx
 |  \/           2*(x - 1)       
 |                               
/                                
1
∫13(6(x−1))32(x−1)+1 dx\int\limits_{1}^{3} \sqrt{\frac{\left(\sqrt{6 \left(x - 1\right)}\right)^{3}}{2 \left(x - 1\right)} + 1}\, dx 
Integral(sqrt(1 + (sqrt(6*(x - 1)))^3/((2*(x - 1)))), (x, 1, 3))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                               
 |                                                                                                                                                                                                                                                                                                                
 |       ____________________                                                                                                                                                                                                                                                                                     
 |      /                  3                                                         ________________________                                                             ________________________                        ________________________                            ________________________            
 |     /        ___________                                   2                     /         ___   ________          2                 ___         5/2                  /         ___   ________          3       ___   /         ___   ________          5/2         ___   /         ___   ________          7/2
 |    /       \/ 6*(x - 1)                          4*(-1 + x)                  4*\/  1 + 3*\/ 6 *\/ -1 + x  *(-1 + x)             12*\/ 6 *(-1 + x)               432*\/  1 + 3*\/ 6 *\/ -1 + x  *(-1 + x)    6*\/ 6 *\/  1 + 3*\/ 6 *\/ -1 + x  *(-1 + x)      972*\/ 6 *\/  1 + 3*\/ 6 *\/ -1 + x  *(-1 + x)   
 |   /    1 + --------------  dx = C + -------------------------------------- - --------------------------------------- + -------------------------------------- + ----------------------------------------- - ----------------------------------------------- + -------------------------------------------------
 | \/           2*(x - 1)                          2          ___         5/2                2          ___         5/2               2          ___         5/2                 2          ___         5/2                     2          ___         5/2                         2          ___         5/2     
 |                                     405*(-1 + x)  + 1215*\/ 6 *(-1 + x)       405*(-1 + x)  + 1215*\/ 6 *(-1 + x)      405*(-1 + x)  + 1215*\/ 6 *(-1 + x)        405*(-1 + x)  + 1215*\/ 6 *(-1 + x)            405*(-1 + x)  + 1215*\/ 6 *(-1 + x)                405*(-1 + x)  + 1215*\/ 6 *(-1 + x)        
/
∫(6(x−1))32(x−1)+1 dx=C+9726(x−1)7236x−1+112156(x−1)52+405(x−1)2−66(x−1)5236x−1+112156(x−1)52+405(x−1)2+126(x−1)5212156(x−1)52+405(x−1)2+432(x−1)336x−1+112156(x−1)52+405(x−1)2−4(x−1)236x−1+112156(x−1)52+405(x−1)2+4(x−1)212156(x−1)52+405(x−1)2\int \sqrt{\frac{\left(\sqrt{6 \left(x - 1\right)}\right)^{3}}{2 \left(x - 1\right)} + 1}\, dx = C + \frac{972 \sqrt{6} \left(x - 1\right)^{\frac{7}{2}} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} - \frac{6 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{12 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{432 \left(x - 1\right)^{3} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} - \frac{4 \left(x - 1\right)^{2} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{4 \left(x - 1\right)^{2}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}}
Simplificar
Gráfica
1.03.01.21.41.61.82.02.22.42.62.8010
Trazar el gráfico f(x)
Respuesta [src] 
                                                _____________                  _____________
                              ___              /         ___            ___   /         ___ 
        16               96*\/ 3        3440*\/  1 + 6*\/ 3     15504*\/ 3 *\/  1 + 6*\/ 3  
----------------- + ----------------- + --------------------- + ----------------------------
              ___                 ___                   ___                        ___      
1620 + 9720*\/ 3    1620 + 9720*\/ 3      1620 + 9720*\/ 3           1620 + 9720*\/ 3
161620+97203+9631620+97203+34401+631620+97203+1550431+631620+97203\frac{16}{1620 + 9720 \sqrt{3}} + \frac{96 \sqrt{3}}{1620 + 9720 \sqrt{3}} + \frac{3440 \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} + \frac{15504 \sqrt{3} \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} 
=
= 
                                                _____________                  _____________
                              ___              /         ___            ___   /         ___ 
        16               96*\/ 3        3440*\/  1 + 6*\/ 3     15504*\/ 3 *\/  1 + 6*\/ 3  
----------------- + ----------------- + --------------------- + ----------------------------
              ___                 ___                   ___                        ___      
1620 + 9720*\/ 3    1620 + 9720*\/ 3      1620 + 9720*\/ 3           1620 + 9720*\/ 3
161620+97203+9631620+97203+34401+631620+97203+1550431+631620+97203\frac{16}{1620 + 9720 \sqrt{3}} + \frac{96 \sqrt{3}}{1620 + 9720 \sqrt{3}} + \frac{3440 \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} + \frac{15504 \sqrt{3} \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} 
16/(1620 + 9720*sqrt(3)) + 96*sqrt(3)/(1620 + 9720*sqrt(3)) + 3440*sqrt(1 + 6*sqrt(3))/(1620 + 9720*sqrt(3)) + 15504*sqrt(3)*sqrt(1 + 6*sqrt(3))/(1620 + 9720*sqrt(3))
Respuesta numérica [src] 
5.55015677502574
5.55015677502574

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

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