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Resolución de integrales/ (3-2x^4+3^sqrt(x6^2))/(4^sqrt(x))

Integral de (3-2x^4+3^sqrt(x6^2))/(4^sqrt(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |                 _____   
 |                /   2    
 |         4    \/  x6     
 |  3 - 2*x  + 3           
 |  -------------------- dx
 |            ___          
 |          \/ x           
 |         4               
 |                         
/                          
0
∫013x62+(3−2x4)4x dx\int\limits_{0}^{1} \frac{3^{\sqrt{x_{6}^{2}}} + \left(3 - 2 x^{4}\right)}{4^{\sqrt{x}}}\, dx 
Integral((3 - 2*x^4 + 3^(sqrt(x6^2)))/4^(sqrt(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                   
 |                                                                                                                                                                                                                                                                                    
 |                _____                                                                                                                                                                                                                                                               
 |               /   2               _____ /       ___        ___      \         ___            ___         ___               ___              ___             ___                ___              ___                ___               ___                   ___            ___      
 |        4    \/  x6               /   2  |    -\/ x      -\/ x    ___|      -\/ x          -\/ x       -\/ x    ___      -\/ x   9/2      -\/ x   4       -\/ x   7/2        -\/ x   3        -\/ x   5/2        -\/ x   2         -\/ x   3/2           -\/ x          -\/ x    ___
 | 3 - 2*x  + 3                   \/  x6   |   4          4      *\/ x |   3*4         2835*4         3*4      *\/ x    2*4      *x      9*4      *x    36*4      *x      126*4      *x    378*4      *x      945*4      *x    1890*4      *x      2835*x*4         2835*4      *\/ x 
 | -------------------- dx = C + 3        *|- --------- - -------------| - --------- + ------------ - --------------- + -------------- + ------------ + --------------- + -------------- + ---------------- + -------------- + ----------------- + -------------- + ------------------
 |           ___                           |       2          log(2)   |        2            10            log(2)           log(2)            2                3                4                 5                 6                  7                 8                  9         
 |         \/ x                            \  2*log (2)                /   2*log (2)    2*log  (2)                                         log (2)          log (2)          log (2)           log (2)           log (2)            log (2)           log (2)            log (2)      
 |        4                                                                                                                                                                                                                                                                           
 |                                                                                                                                                                                                                                                                                    
/
∫3x62+(3−2x4)4x dx=3x62(−4−xxlog⁡(2)−4−x2log⁡(2)2)+C+2⋅4−xx92log⁡(2)+36⋅4−xx72log⁡(2)3+378⋅4−xx52log⁡(2)5+1890⋅4−xx32log⁡(2)7−3⋅4−xxlog⁡(2)+2835⋅4−xxlog⁡(2)9+9⋅4−xx4log⁡(2)2+126⋅4−xx3log⁡(2)4+945⋅4−xx2log⁡(2)6+2835⋅4−xxlog⁡(2)8−3⋅4−x2log⁡(2)2+2835⋅4−x2log⁡(2)10\int \frac{3^{\sqrt{x_{6}^{2}}} + \left(3 - 2 x^{4}\right)}{4^{\sqrt{x}}}\, dx = 3^{\sqrt{x_{6}^{2}}} \left(- \frac{4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}} - \frac{4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{2}}\right) + C + \frac{2 \cdot 4^{- \sqrt{x}} x^{\frac{9}{2}}}{\log{\left(2 \right)}} + \frac{36 \cdot 4^{- \sqrt{x}} x^{\frac{7}{2}}}{\log{\left(2 \right)}^{3}} + \frac{378 \cdot 4^{- \sqrt{x}} x^{\frac{5}{2}}}{\log{\left(2 \right)}^{5}} + \frac{1890 \cdot 4^{- \sqrt{x}} x^{\frac{3}{2}}}{\log{\left(2 \right)}^{7}} - \frac{3 \cdot 4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}} + \frac{2835 \cdot 4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}^{9}} + \frac{9 \cdot 4^{- \sqrt{x}} x^{4}}{\log{\left(2 \right)}^{2}} + \frac{126 \cdot 4^{- \sqrt{x}} x^{3}}{\log{\left(2 \right)}^{4}} + \frac{945 \cdot 4^{- \sqrt{x}} x^{2}}{\log{\left(2 \right)}^{6}} + \frac{2835 \cdot 4^{- \sqrt{x}} x}{\log{\left(2 \right)}^{8}} - \frac{3 \cdot 4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{2}} + \frac{2835 \cdot 4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{10}}
Simplificar
Respuesta [src] 
                                                                                                                          _____         _____
                                                                                                                         /   2         /   2 
                                                                                                                       \/  x6        \/  x6  
   9         8505         1           27          63         189         945         945         2835        2835     3           3*3        
------- - ---------- - -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- - --------- + -----------
   3           10      4*log(2)        2           4           5           7           6           9           8       4*log(2)         2    
log (2)   8*log  (2)              8*log (2)   2*log (2)   2*log (2)   2*log (2)   4*log (2)   4*log (2)   4*log (2)                8*log (2)
−3x624log⁡(2)+3⋅3x628log⁡(2)2−85058log⁡(2)10−14log⁡(2)+278log⁡(2)2+9log⁡(2)3+632log⁡(2)4+1892log⁡(2)5+9454log⁡(2)6+9452log⁡(2)7+28354log⁡(2)8+28354log⁡(2)9- \frac{3^{\sqrt{x_{6}^{2}}}}{4 \log{\left(2 \right)}} + \frac{3 \cdot 3^{\sqrt{x_{6}^{2}}}}{8 \log{\left(2 \right)}^{2}} - \frac{8505}{8 \log{\left(2 \right)}^{10}} - \frac{1}{4 \log{\left(2 \right)}} + \frac{27}{8 \log{\left(2 \right)}^{2}} + \frac{9}{\log{\left(2 \right)}^{3}} + \frac{63}{2 \log{\left(2 \right)}^{4}} + \frac{189}{2 \log{\left(2 \right)}^{5}} + \frac{945}{4 \log{\left(2 \right)}^{6}} + \frac{945}{2 \log{\left(2 \right)}^{7}} + \frac{2835}{4 \log{\left(2 \right)}^{8}} + \frac{2835}{4 \log{\left(2 \right)}^{9}} 
=
= 
                                                                                                                          _____         _____
                                                                                                                         /   2         /   2 
                                                                                                                       \/  x6        \/  x6  
   9         8505         1           27          63         189         945         945         2835        2835     3           3*3        
------- - ---------- - -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- - --------- + -----------
   3           10      4*log(2)        2           4           5           7           6           9           8       4*log(2)         2    
log (2)   8*log  (2)              8*log (2)   2*log (2)   2*log (2)   2*log (2)   4*log (2)   4*log (2)   4*log (2)                8*log (2)
−3x624log⁡(2)+3⋅3x628log⁡(2)2−85058log⁡(2)10−14log⁡(2)+278log⁡(2)2+9log⁡(2)3+632log⁡(2)4+1892log⁡(2)5+9454log⁡(2)6+9452log⁡(2)7+28354log⁡(2)8+28354log⁡(2)9- \frac{3^{\sqrt{x_{6}^{2}}}}{4 \log{\left(2 \right)}} + \frac{3 \cdot 3^{\sqrt{x_{6}^{2}}}}{8 \log{\left(2 \right)}^{2}} - \frac{8505}{8 \log{\left(2 \right)}^{10}} - \frac{1}{4 \log{\left(2 \right)}} + \frac{27}{8 \log{\left(2 \right)}^{2}} + \frac{9}{\log{\left(2 \right)}^{3}} + \frac{63}{2 \log{\left(2 \right)}^{4}} + \frac{189}{2 \log{\left(2 \right)}^{5}} + \frac{945}{4 \log{\left(2 \right)}^{6}} + \frac{945}{2 \log{\left(2 \right)}^{7}} + \frac{2835}{4 \log{\left(2 \right)}^{8}} + \frac{2835}{4 \log{\left(2 \right)}^{9}} 
9/log(2)^3 - 8505/(8*log(2)^10) - 1/(4*log(2)) + 27/(8*log(2)^2) + 63/(2*log(2)^4) + 189/(2*log(2)^5) + 945/(2*log(2)^7) + 945/(4*log(2)^6) + 2835/(4*log(2)^9) + 2835/(4*log(2)^8) - 3^(sqrt(x6^2))/(4*log(2)) + 3*3^(sqrt(x6^2))/(8*log(2)^2)

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

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