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Resolución de integrales/ sqrt5/ x/(sqrt5-x^4)

Integral de x/(sqrt5-x^4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      x        
 |  ---------- dx
 |    ___    4   
 |  \/ 5  - x    
 |               
/                
0
$$\int\limits_{0}^{1} \frac{x}{- x^{4} + \sqrt{5}}\, dx$$ 
Integral(x/(sqrt(5) - x^4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                       //           / 3/4  2\                 \
                       ||  3/4      |5   *x |                 |
                       ||-5   *acoth|-------|                 |
  /                    ||           \   5   /        4     ___|
 |                     ||---------------------  for x  > \/ 5 |
 |     x               ||          10                         |
 | ---------- dx = C - |<                                     |
 |   ___    4          ||           / 3/4  2\                 |
 | \/ 5  - x           ||  3/4      |5   *x |                 |
 |                     ||-5   *atanh|-------|                 |
/                      ||           \   5   /        4     ___|
                       ||---------------------  for x  < \/ 5 |
                       \\          10                         /
$$\int \frac{x}{- x^{4} + \sqrt{5}}\, dx = C - \begin{cases} - \frac{5^{\frac{3}{4}} \operatorname{acoth}{\left(\frac{5^{\frac{3}{4}} x^{2}}{5} \right)}}{10} & \text{for}\: x^{4} > \sqrt{5} \\- \frac{5^{\frac{3}{4}} \operatorname{atanh}{\left(\frac{5^{\frac{3}{4}} x^{2}}{5} \right)}}{10} & \text{for}\: x^{4} < \sqrt{5} \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   3/4 /          /     4 ___\\    3/4    /4 ___\    3/4 /          /4 ___\\    3/4    /    4 ___\
  5   *\pi*I + log\-1 + \/ 5 //   5   *log\\/ 5 /   5   *\pi*I + log\\/ 5 //   5   *log\1 + \/ 5 /
- ----------------------------- - --------------- + ------------------------ + -------------------
                20                       20                    20                       20
$$- \frac{5^{\frac{3}{4}} \log{\left(\sqrt[4]{5} \right)}}{20} + \frac{5^{\frac{3}{4}} \log{\left(1 + \sqrt[4]{5} \right)}}{20} - \frac{5^{\frac{3}{4}} \left(\log{\left(-1 + \sqrt[4]{5} \right)} + i \pi\right)}{20} + \frac{5^{\frac{3}{4}} \left(\log{\left(\sqrt[4]{5} \right)} + i \pi\right)}{20}$$ 
=
= 
   3/4 /          /     4 ___\\    3/4    /4 ___\    3/4 /          /4 ___\\    3/4    /    4 ___\
  5   *\pi*I + log\-1 + \/ 5 //   5   *log\\/ 5 /   5   *\pi*I + log\\/ 5 //   5   *log\1 + \/ 5 /
- ----------------------------- - --------------- + ------------------------ + -------------------
                20                       20                    20                       20
$$- \frac{5^{\frac{3}{4}} \log{\left(\sqrt[4]{5} \right)}}{20} + \frac{5^{\frac{3}{4}} \log{\left(1 + \sqrt[4]{5} \right)}}{20} - \frac{5^{\frac{3}{4}} \left(\log{\left(-1 + \sqrt[4]{5} \right)} + i \pi\right)}{20} + \frac{5^{\frac{3}{4}} \left(\log{\left(\sqrt[4]{5} \right)} + i \pi\right)}{20}$$ 
-5^(3/4)*(pi*i + log(-1 + 5^(1/4)))/20 - 5^(3/4)*log(5^(1/4))/20 + 5^(3/4)*(pi*i + log(5^(1/4)))/20 + 5^(3/4)*log(1 + 5^(1/4))/20
Respuesta numérica [src] 
0.270325172263721
0.270325172263721

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

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