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Resolución de integrales/ 5*x^4/ dx/(4+25*x^4)

Integral de dx/(4+25*x^4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |      1       
 |  --------- dx
 |          4   
 |  4 + 25*x    
 |              
/               
0
∫01125x4+4 dx\int\limits_{0}^{1} \frac{1}{25 x^{4} + 4}\, dx 
Integral(1/(4 + 25*x^4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               /               ___\                                                                 /               ___\
  /                     ___    |2    2   2*x*\/ 5 |                                                          ___    |2    2   2*x*\/ 5 |
 |                    \/ 5 *log|- + x  - ---------|     ___     /        ___\     ___     /         ___\   \/ 5 *log|- + x  + ---------|
 |     1                       \5            5    /   \/ 5 *atan\1 + x*\/ 5 /   \/ 5 *atan\-1 + x*\/ 5 /            \5            5    /
 | --------- dx = C - ----------------------------- + ----------------------- + ------------------------ + -----------------------------
 |         4                        80                           40                        40                            80             
 | 4 + 25*x                                                                                                                             
 |                                                                                                                                      
/
∫125x4+4 dx=C−5log⁡(x2−25x5+25)80+5log⁡(x2+25x5+25)80+5atan⁡(5x−1)40+5atan⁡(5x+1)40\int \frac{1}{25 x^{4} + 4}\, dx = C - \frac{\sqrt{5} \log{\left(x^{2} - \frac{2 \sqrt{5} x}{5} + \frac{2}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{2 \sqrt{5} x}{5} + \frac{2}{5} \right)}}{80} + \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} x - 1 \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} x + 1 \right)}}{40}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000.50
Trazar el gráfico f(x)
Respuesta [src] 
                                   /        ___\                                    /        ___\
                            ___    |7   2*\/ 5 |                             ___    |7   2*\/ 5 |
    ___     /      ___\   \/ 5 *log|- - -------|     ___     /      ___\   \/ 5 *log|- + -------|
  \/ 5 *atan\1 - \/ 5 /            \5      5   /   \/ 5 *atan\1 + \/ 5 /            \5      5   /
- --------------------- - ---------------------- + --------------------- + ----------------------
            40                      80                       40                      80
−5log⁡(75−255)80+5log⁡(255+75)80−5atan⁡(1−5)40+5atan⁡(1+5)40- \frac{\sqrt{5} \log{\left(\frac{7}{5} - \frac{2 \sqrt{5}}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(\frac{2 \sqrt{5}}{5} + \frac{7}{5} \right)}}{80} - \frac{\sqrt{5} \operatorname{atan}{\left(1 - \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(1 + \sqrt{5} \right)}}{40} 
=
= 
                                   /        ___\                                    /        ___\
                            ___    |7   2*\/ 5 |                             ___    |7   2*\/ 5 |
    ___     /      ___\   \/ 5 *log|- - -------|     ___     /      ___\   \/ 5 *log|- + -------|
  \/ 5 *atan\1 - \/ 5 /            \5      5   /   \/ 5 *atan\1 + \/ 5 /            \5      5   /
- --------------------- - ---------------------- + --------------------- + ----------------------
            40                      80                       40                      80
−5log⁡(75−255)80+5log⁡(255+75)80−5atan⁡(1−5)40+5atan⁡(1+5)40- \frac{\sqrt{5} \log{\left(\frac{7}{5} - \frac{2 \sqrt{5}}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(\frac{2 \sqrt{5}}{5} + \frac{7}{5} \right)}}{80} - \frac{\sqrt{5} \operatorname{atan}{\left(1 - \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(1 + \sqrt{5} \right)}}{40} 
-sqrt(5)*atan(1 - sqrt(5))/40 - sqrt(5)*log(7/5 - 2*sqrt(5)/5)/80 + sqrt(5)*atan(1 + sqrt(5))/40 + sqrt(5)*log(7/5 + 2*sqrt(5)/5)/80
Respuesta numérica [src] 
0.16311793324958
0.16311793324958

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

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