Sr Examen

Otras calculadoras

Integral de x^3*dx/(4+x^6) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1          
  /          
 |           
 |     3     
 |    x      
 |  ------ dx
 |       6   
 |  4 + x    
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{x^{3}}{x^{6} + 4}\, dx$$
Integral(x^3/(4 + x^6), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                                                                           /    ___   3 ___   ___  2\
 |                                                                            3 ___   ___     |  \/ 3    \/ 2 *\/ 3 *x |
 |    3            3 ___    / 2/3    2\   3 ___    / 4     3 ___    2/3  2\   \/ 2 *\/ 3 *atan|- ----- + --------------|
 |   x             \/ 2 *log\2    + x /   \/ 2 *log\x  + 2*\/ 2  - 2   *x /                   \    3           3       /
 | ------ dx = C - -------------------- + --------------------------------- + ------------------------------------------
 |      6                   12                            24                                      12                    
 | 4 + x                                                                                                                
 |                                                                                                                      
/                                                                                                                       
$$\int \frac{x^{3}}{x^{6} + 4}\, dx = C - \frac{\sqrt[3]{2} \log{\left(x^{2} + 2^{\frac{2}{3}} \right)}}{12} + \frac{\sqrt[3]{2} \log{\left(x^{4} - 2^{\frac{2}{3}} x^{2} + 2 \sqrt[3]{2} \right)}}{24} + \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}$$
Gráfica
Respuesta [src]
                                                                                                               /  ___   3 ___   ___\                 
                                                                                               3 ___   ___     |\/ 3    \/ 2 *\/ 3 |                 
  3 ___    /     2/3\   3 ___    /  3 ___\   3 ___    / 2/3\   3 ___    /     2/3     3 ___\   \/ 2 *\/ 3 *atan|----- - -----------|      3 ___   ___
  \/ 2 *log\1 + 2   /   \/ 2 *log\2*\/ 2 /   \/ 2 *log\2   /   \/ 2 *log\1 - 2    + 2*\/ 2 /                   \  3          3     /   pi*\/ 2 *\/ 3 
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
           12                   24                  12                       24                                  12                          72      
$$- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{12} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{24} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{24} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{12} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{72}$$
=
=
                                                                                                               /  ___   3 ___   ___\                 
                                                                                               3 ___   ___     |\/ 3    \/ 2 *\/ 3 |                 
  3 ___    /     2/3\   3 ___    /  3 ___\   3 ___    / 2/3\   3 ___    /     2/3     3 ___\   \/ 2 *\/ 3 *atan|----- - -----------|      3 ___   ___
  \/ 2 *log\1 + 2   /   \/ 2 *log\2*\/ 2 /   \/ 2 *log\2   /   \/ 2 *log\1 - 2    + 2*\/ 2 /                   \  3          3     /   pi*\/ 2 *\/ 3 
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
           12                   24                  12                       24                                  12                          72      
$$- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{12} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{24} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{24} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{12} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{72}$$
-2^(1/3)*log(1 + 2^(2/3))/12 - 2^(1/3)*log(2*2^(1/3))/24 + 2^(1/3)*log(2^(2/3))/12 + 2^(1/3)*log(1 - 2^(2/3) + 2*2^(1/3))/24 - 2^(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2^(1/3)*sqrt(3)/3)/12 + pi*2^(1/3)*sqrt(3)/72
Respuesta numérica [src]
0.0570779564233563
0.0570779564233563

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