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  • Expresiones idénticas

  • x^2dx/(cinco x^ cuatro + siete)^5
  • x al cuadrado dx dividir por (5x en el grado 4 más 7) en el grado 5
  • x al cuadrado dx dividir por (cinco x en el grado cuatro más siete) en el grado 5
  • x2dx/(5x4+7)5
  • x2dx/5x4+75
  • x²dx/(5x⁴+7)⁵
  • x en el grado 2dx/(5x en el grado 4+7) en el grado 5
  • x^2dx/5x^4+7^5
  • x^2dx dividir por (5x^4+7)^5

  • Expresiones semejantes

  • x^2dx/(5x^4-7)^5
Resolución de integrales/ x^2dx/ x^2dx/(5x^4+7)^5

Integral de x^2dx/(5x^4+7)^5 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |        2       
 |       x        
 |  ----------- dx
 |            5   
 |  /   4    \    
 |  \5*x  + 7/    
 |                
/                 
0
∫01x2(5x4+7)5 dx\int\limits_{0}^{1} \frac{x^{2}}{\left(5 x^{4} + 7\right)^{5}}\, dx 
Integral(x^2/(5*x^4 + 7)^5, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                /        ___ 4 ______\                         /         ___ 4 ______\                          /       ____       ___  3/4 4 ___\                          /       ____       ___  3/4 4 ___\
 |                                                                                                                ___ 4 ______     |    x*\/ 2 *\/ 1715 |        ___ 4 ______     |     x*\/ 2 *\/ 1715 |        ___ 4 ___  3/4    | 2   \/ 35    x*\/ 2 *5   *\/ 7 |        ___ 4 ___  3/4    | 2   \/ 35    x*\/ 2 *5   *\/ 7 |
 |       2                                       15           11           3           7                     39*\/ 2 *\/ 1715 *atan|1 + ----------------|   39*\/ 2 *\/ 1715 *atan|-1 + ----------------|   39*\/ 2 *\/ 5 *7   *log|x  + ------ + ------------------|   39*\/ 2 *\/ 5 *7   *log|x  + ------ - ------------------|
 |      x                                 73125*x   + 389025*x   + 635579*x  + 761215*x                                            \           7        /                         \            7        /                          \       5              5         /                          \       5              5         /
 | ----------- dx = C + ---------------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------- - --------------------------------------------------------- + ---------------------------------------------------------
 |           5                                    16                12                 4                 8                    137682944                                       137682944                                             275365888                                                   275365888                        
 | /   4    \           35418937344 + 9219840000*x   + 51631104000*x   + 101196963840*x  + 108425318400*x                                                                                                                                                                                                                        
 | \5*x  + 7/                                                                                                                                                                                                                                                                                                                    
 |                                                                                                                                                                                                                                                                                                                               
/
∫x2(5x4+7)5 dx=C+73125x15+389025x11+761215x7+635579x39219840000x16+51631104000x12+108425318400x8+101196963840x4+35418937344+39254⋅734log⁡(x2−2⋅53474x5+355)275365888−39254⋅734log⁡(x2+2⋅53474x5+355)275365888+39171542atan⁡(171542x7−1)137682944+39171542atan⁡(171542x7+1)137682944\int \frac{x^{2}}{\left(5 x^{4} + 7\right)^{5}}\, dx = C + \frac{73125 x^{15} + 389025 x^{11} + 761215 x^{7} + 635579 x^{3}}{9219840000 x^{16} + 51631104000 x^{12} + 108425318400 x^{8} + 101196963840 x^{4} + 35418937344} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(x^{2} - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7} x}{5} + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(x^{2} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7} x}{5} + \frac{\sqrt{35}}{5} \right)}}{275365888} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} \sqrt{2} x}{7} - 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} \sqrt{2} x}{7} + 1 \right)}}{137682944}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000000.00002
Trazar el gráfico f(x)
Respuesta [src] 
                                  /      ___ 4 ______\                         /      ___ 4 ______\                          /      ____     ___  3/4 4 ___\                          /      ____     ___  3/4 4 ___\
                 ___ 4 ______     |    \/ 2 *\/ 1715 |        ___ 4 ______     |    \/ 2 *\/ 1715 |        ___ 4 ___  3/4    |    \/ 35    \/ 2 *5   *\/ 7 |        ___ 4 ___  3/4    |    \/ 35    \/ 2 *5   *\/ 7 |
            39*\/ 2 *\/ 1715 *atan|1 - --------------|   39*\/ 2 *\/ 1715 *atan|1 + --------------|   39*\/ 2 *\/ 5 *7   *log|1 + ------ + ----------------|   39*\/ 2 *\/ 5 *7   *log|1 + ------ - ----------------|
   4841                           \          7       /                         \          7       /                          \      5             5        /                          \      5             5        /
--------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------
796594176                   137682944                                    137682944                                          275365888                                                275365888
−39254⋅734log⁡(1+355+2⋅534745)275365888+39254⋅734log⁡(−2⋅534745+1+355)275365888−39171542atan⁡(−1715427+1)137682944+39171542atan⁡(1+1715427)137682944+4841796594176- \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(1 + \frac{\sqrt{35}}{5} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} \right)}}{275365888} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} + 1 + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt[4]{1715} \sqrt{2}}{7} + 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\sqrt[4]{1715} \sqrt{2}}{7} \right)}}{137682944} + \frac{4841}{796594176} 
=
= 
                                  /      ___ 4 ______\                         /      ___ 4 ______\                          /      ____     ___  3/4 4 ___\                          /      ____     ___  3/4 4 ___\
                 ___ 4 ______     |    \/ 2 *\/ 1715 |        ___ 4 ______     |    \/ 2 *\/ 1715 |        ___ 4 ___  3/4    |    \/ 35    \/ 2 *5   *\/ 7 |        ___ 4 ___  3/4    |    \/ 35    \/ 2 *5   *\/ 7 |
            39*\/ 2 *\/ 1715 *atan|1 - --------------|   39*\/ 2 *\/ 1715 *atan|1 + --------------|   39*\/ 2 *\/ 5 *7   *log|1 + ------ + ----------------|   39*\/ 2 *\/ 5 *7   *log|1 + ------ - ----------------|
   4841                           \          7       /                         \          7       /                          \      5             5        /                          \      5             5        /
--------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------
796594176                   137682944                                    137682944                                          275365888                                                275365888
−39254⋅734log⁡(1+355+2⋅534745)275365888+39254⋅734log⁡(−2⋅534745+1+355)275365888−39171542atan⁡(−1715427+1)137682944+39171542atan⁡(1+1715427)137682944+4841796594176- \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(1 + \frac{\sqrt{35}}{5} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} \right)}}{275365888} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} + 1 + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt[4]{1715} \sqrt{2}}{7} + 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\sqrt[4]{1715} \sqrt{2}}{7} \right)}}{137682944} + \frac{4841}{796594176} 
4841/796594176 - 39*sqrt(2)*1715^(1/4)*atan(1 - sqrt(2)*1715^(1/4)/7)/137682944 + 39*sqrt(2)*1715^(1/4)*atan(1 + sqrt(2)*1715^(1/4)/7)/137682944 - 39*sqrt(2)*5^(1/4)*7^(3/4)*log(1 + sqrt(35)/5 + sqrt(2)*5^(3/4)*7^(1/4)/5)/275365888 + 39*sqrt(2)*5^(1/4)*7^(3/4)*log(1 + sqrt(35)/5 - sqrt(2)*5^(3/4)*7^(1/4)/5)/275365888
Respuesta numérica [src] 
7.56160655711879e-6
7.56160655711879e-6

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

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