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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |   2*x     
 |  ------ dx
 |       3   
 |  4 + x    
 |           
/            
0
∫012xx3+4 dx\int\limits_{0}^{1} \frac{2 x}{x^{3} + 4}\, dx 
Integral((2*x)/(4 + x^3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                            /    ___     3 ___   ___\
  /                                                                         3 ___   ___     |  \/ 3    x*\/ 2 *\/ 3 |
 |                 3 ___    /     2/3\   3 ___    / 2     3 ___      2/3\   \/ 2 *\/ 3 *atan|- ----- + -------------|
 |  2*x            \/ 2 *log\x + 2   /   \/ 2 *log\x  + 2*\/ 2  - x*2   /                   \    3           3      /
 | ------ dx = C - ------------------- + -------------------------------- + -----------------------------------------
 |      3                   3                           6                                       3                    
 | 4 + x                                                                                                             
 |                                                                                                                   
/
∫2xx3+4 dx=C−23log⁡(x+223)3+23log⁡(x2−223x+223)6+233atan⁡(233x3−33)3\int \frac{2 x}{x^{3} + 4}\, dx = C - \frac{\sqrt[3]{2} \log{\left(x + 2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(x^{2} - 2^{\frac{2}{3}} x + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901.0-1.0
Trazar el gráfico f(x)
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 
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
           3                    6                   3                        6                                   3                           18
−23log⁡(1+223)3−23log⁡(223)6−233atan⁡(−2333+33)3+23log⁡(−223+1+223)6+23log⁡(223)3+233π18- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{3} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{6} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{18} 
=
= 
                                                                                                               /  ___   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 
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
           3                    6                   3                        6                                   3                           18
−23log⁡(1+223)3−23log⁡(223)6−233atan⁡(−2333+33)3+23log⁡(−223+1+223)6+23log⁡(223)3+233π18- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{3} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{6} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{18} 
-2^(1/3)*log(1 + 2^(2/3))/3 - 2^(1/3)*log(2*2^(1/3))/6 + 2^(1/3)*log(2^(2/3))/3 + 2^(1/3)*log(1 - 2^(2/3) + 2*2^(1/3))/6 - 2^(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2^(1/3)*sqrt(3)/3)/3 + pi*2^(1/3)*sqrt(3)/18
Respuesta numérica [src] 
0.228311825693425
0.228311825693425

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

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