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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |        x         
 |  ------------- dx
 |     __________   
 |    /      2/3    
 |  \/  2 + x       
 |                  
/                   
0
∫01xx23+2 dx\int\limits_{0}^{1} \frac{x}{\sqrt{x^{\frac{2}{3}} + 2}}\, dx 
Integral(x/sqrt(2 + x^(2/3)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                           __________                                                    __________                                                 __________                                                     __________                                                  __________                                                    __________               
 |                                                     20/3                                                           6                                                          22/3                                                          8                                                 ___  28/3   /      2/3                                        ___  26/3   /      2/3                                        ___  8   /      2/3                                         ___  22/3   /      2/3                                         ___  6   /      2/3                                        ___  20/3   /      2/3                
 |       x                                        768*x                                                          512*x                                                      384*x                                                          64*x                                              3*\/ 2 *x    *\/  2 + x                                      10*\/ 2 *x    *\/  2 + x                                      20*\/ 2 *x *\/  2 + x                                      120*\/ 2 *x    *\/  2 + x                                      256*\/ 2 *x *\/  2 + x                                     320*\/ 2 *x    *\/  2 + x                   
 | ------------- dx = C - ---------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- + ---------------------------------------------------------- + ---------------------------------------------------------- + ---------------------------------------------------------- + ---------------------------------------------------------- + ---------------------------------------------------------- + ----------------------------------------------------------
 |    __________              ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3       ___  8        ___  22/3        ___  6        ___  20/3
 |   /      2/3           5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x       5*\/ 2 *x  + 30*\/ 2 *x     + 40*\/ 2 *x  + 60*\/ 2 *x    
 | \/  2 + x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
/
∫xx23+2 dx=C+32x283x23+2302x223+602x203+52x8+402x6+102x263x23+2302x223+602x203+52x8+402x6+1202x223x23+2302x223+602x203+52x8+402x6−384x223302x223+602x203+52x8+402x6+3202x203x23+2302x223+602x203+52x8+402x6−768x203302x223+602x203+52x8+402x6+202x8x23+2302x223+602x203+52x8+402x6−64x8302x223+602x203+52x8+402x6+2562x6x23+2302x223+602x203+52x8+402x6−512x6302x223+602x203+52x8+402x6\int \frac{x}{\sqrt{x^{\frac{2}{3}} + 2}}\, dx = C + \frac{3 \sqrt{2} x^{\frac{28}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{10 \sqrt{2} x^{\frac{26}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{120 \sqrt{2} x^{\frac{22}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{384 x^{\frac{22}{3}}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{320 \sqrt{2} x^{\frac{20}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{768 x^{\frac{20}{3}}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{20 \sqrt{2} x^{8} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{64 x^{8}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{256 \sqrt{2} x^{6} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{512 x^{6}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta numérica [src] 
0.302107561684129
0.302107561684129

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

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