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Resolución de integrales/ -5x^4/ -3x^2/ 2x-3x/ (2x-3x^2)/(7-5x^4)

Integral de (2x-3x^2)/(7-5x^4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |           2   
 |  2*x - 3*x    
 |  ---------- dx
 |          4    
 |   7 - 5*x     
 |               
/                
0
∫01−3x2+2x7−5x4 dx\int\limits_{0}^{1} \frac{- 3 x^{2} + 2 x}{7 - 5 x^{4}}\, dx 
Integral((2*x - 3*x^2)/(7 - 5*x^4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //             /  ____  2\               \                                                                                          
                         ||   ____      |\/ 35 *x |               |                                                                                          
  /                      ||-\/ 35 *acoth|---------|               |                 /    4 _____\                  /  4 ______\                 /    4 _____\
 |                       ||             \    7    /        4      |     4 ______    |    \/ 875 |     4 ______     |x*\/ 1715 |     4 ______    |    \/ 875 |
 |          2            ||-------------------------  for x  > 7/5|   3*\/ 1715 *log|x + -------|   3*\/ 1715 *atan|----------|   3*\/ 1715 *log|x - -------|
 | 2*x - 3*x             ||            70                         |                 \       5   /                  \    7     /                 \       5   /
 | ---------- dx = C - 2*|<                                       | - --------------------------- + --------------------------- + ---------------------------
 |         4             ||             /  ____  2\               |               140                            70                           140            
 |  7 - 5*x              ||   ____      |\/ 35 *x |               |                                                                                          
 |                       ||-\/ 35 *atanh|---------|               |                                                                                          
/                        ||             \    7    /        4      |                                                                                          
                         ||-------------------------  for x  < 7/5|                                                                                          
                         \\            70                         /
∫−3x2+2x7−5x4 dx=C−2({−35acoth⁡(35x27)70for x4>75−35atanh⁡(35x27)70for x4<75)+317154log⁡(x−87545)140−317154log⁡(x+87545)140+317154atan⁡(17154x7)70\int \frac{- 3 x^{2} + 2 x}{7 - 5 x^{4}}\, dx = C - 2 \left(\begin{cases} - \frac{\sqrt{35} \operatorname{acoth}{\left(\frac{\sqrt{35} x^{2}}{7} \right)}}{70} & \text{for}\: x^{4} > \frac{7}{5} \\- \frac{\sqrt{35} \operatorname{atanh}{\left(\frac{\sqrt{35} x^{2}}{7} \right)}}{70} & \text{for}\: x^{4} < \frac{7}{5} \end{cases}\right) + \frac{3 \sqrt[4]{1715} \log{\left(x - \frac{\sqrt[4]{875}}{5} \right)}}{140} - \frac{3 \sqrt[4]{1715} \log{\left(x + \frac{\sqrt[4]{875}}{5} \right)}}{140} + \frac{3 \sqrt[4]{1715} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} x}{7} \right)}}{70}
Simplificar
Respuesta [src] 
         /                                                 /                 3                   2\\          /                                                 /                 3                   2\\
         |         4          2                            |  3722   235200*t    5040*t   44800*t ||          |         4          2                            |  1061   235200*t    5040*t   44800*t ||
- RootSum|1568000*t  - 22400*t  + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------|| + RootSum|1568000*t  - 22400*t  + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------||
         \                                                 \  2661      887       887       2661  //          \                                                 \  2661      887       887       2661  //
−RootSum⁡(1568000t4−22400t2+10080t−487,(t↦tlog⁡(−235200t3887+44800t22661+5040t887−37222661)))+RootSum⁡(1568000t4−22400t2+10080t−487,(t↦tlog⁡(−235200t3887+44800t22661+5040t887−10612661)))- \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{3722}{2661} \right)} \right)\right)} + \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{1061}{2661} \right)} \right)\right)} 
=
= 
         /                                                 /                 3                   2\\          /                                                 /                 3                   2\\
         |         4          2                            |  3722   235200*t    5040*t   44800*t ||          |         4          2                            |  1061   235200*t    5040*t   44800*t ||
- RootSum|1568000*t  - 22400*t  + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------|| + RootSum|1568000*t  - 22400*t  + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------||
         \                                                 \  2661      887       887       2661  //          \                                                 \  2661      887       887       2661  //
−RootSum⁡(1568000t4−22400t2+10080t−487,(t↦tlog⁡(−235200t3887+44800t22661+5040t887−37222661)))+RootSum⁡(1568000t4−22400t2+10080t−487,(t↦tlog⁡(−235200t3887+44800t22661+5040t887−10612661)))- \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{3722}{2661} \right)} \right)\right)} + \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{1061}{2661} \right)} \right)\right)} 
-RootSum(1568000*_t^4 - 22400*_t^2 + 10080*_t - 487, Lambda(_t, _t*log(-3722/2661 - 235200*_t^3/887 + 5040*_t/887 + 44800*_t^2/2661))) + RootSum(1568000*_t^4 - 22400*_t^2 + 10080*_t - 487, Lambda(_t, _t*log(-1061/2661 - 235200*_t^3/887 + 5040*_t/887 + 44800*_t^2/2661)))
Respuesta numérica [src] 
-0.0225933258028005
-0.0225933258028005

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

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