Sr Examen

Otras calculadoras

Resolución de integrales/ (3x^2+x-2)/(2x^7+3x^5-x^2-1)

Integral de (3x^2+x-2)/(2x^7+3x^5-x^2-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                        
  /                        
 |                         
 |         2               
 |      3*x  + x - 2       
 |  -------------------- dx
 |     7      5    2       
 |  2*x  + 3*x  - x  - 1   
 |                         
/                          
1
∫1∞(3x2+x)−2(−x2+(2x7+3x5))−1 dx\int\limits_{1}^{\infty} \frac{\left(3 x^{2} + x\right) - 2}{\left(- x^{2} + \left(2 x^{7} + 3 x^{5}\right)\right) - 1}\, dx 
Integral((3*x^2 + x - 2)/(2*x^7 + 3*x^5 - x^2 - 1), (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
 |        2                               /                                                                            /                                                        6                             3                            2                                                        4                              5\\            /                                                                         /                                                       6                             5                         2                                                    3                            4\\          /                                                                          /                                                           6                              4                              5                             2                                                         3\\
 |     3*x  + x - 2                       |         7          5          4          3        2                        |925428188882900899657       72277241424336888589729529*t    437989287638021185973565*t    27613275754890251531439*t    25709295147507149852993*t   31182985334944362544409*t    2549382420526595647929629*t ||            |         7           5         4         3       2                       |  5978319999868176713       1338254223722234609519895*t    141607889991322281135329*t    79086989811432346138*t    39993172691320168133*t   7121143425189507540611*t    16779000163258668460573*t ||          |         7          5          4         3        2                       |  458764957683141536262       158367799939777137068438427*t    4118014325496337342677133*t    3208271250789907217809437*t    121941987059033803462821*t    14998806734791161779739*t   282755219073426871910893*t ||
 | -------------------- dx = C - 2*RootSum|6219033*t  - 35009*t  + 74300*t  + 10134*t  - 395*t  - 108*t - 4, t -> t*log|--------------------- + x - ----------------------------- - --------------------------- - -------------------------- + ------------------------- + -------------------------- + ----------------------------|| + 3*RootSum|6219033*t  - 145850*t  - 2622*t  + 1213*t  - 85*t  + 18*t - 1, t -> t*log|- ------------------- + x - ---------------------------- - --------------------------- - ----------------------- + ---------------------- + ------------------------- + --------------------------|| + RootSum|6219033*t  + 86245*t  - 25115*t  + 5155*t  - 551*t  + 42*t - 2, t -> t*log|- --------------------- + x - ------------------------------ - ---------------------------- - ---------------------------- - --------------------------- + ------------------------- + ---------------------------||
 |    7      5    2                       \                                                                            \ 55170589054432541466            36780392702955027644           18390196351477513822         18390196351477513822        110341178108865082932        15763025444123583276          18390196351477513822    //            \                                                                         \  1842512986976738322            614170995658912774             614170995658912774          921256493488369161      1842512986976738322        1842512986976738322          614170995658912774    //          \                                                                          \  388656885842700080081           777313771685400160162           777313771685400160162          388656885842700080081          777313771685400160162        777313771685400160162        777313771685400160162   //
 | 2*x  + 3*x  - x  - 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
/
∫(3x2+x)−2(−x2+(2x7+3x5))−1 dx=C+3RootSum⁡(6219033t7−145850t5−2622t4+1213t3−85t2+18t−1,(t↦tlog⁡(−1338254223722234609519895t6614170995658912774−141607889991322281135329t5614170995658912774+16779000163258668460573t4614170995658912774+7121143425189507540611t31842512986976738322−79086989811432346138t2921256493488369161+39993172691320168133t1842512986976738322+x−59783199998681767131842512986976738322)))+RootSum⁡(6219033t7+86245t5−25115t4+5155t3−551t2+42t−2,(t↦tlog⁡(−158367799939777137068438427t6777313771685400160162−3208271250789907217809437t5388656885842700080081−4118014325496337342677133t4777313771685400160162+282755219073426871910893t3777313771685400160162−121941987059033803462821t2777313771685400160162+14998806734791161779739t777313771685400160162+x−458764957683141536262388656885842700080081)))−2RootSum⁡(6219033t7−35009t5+74300t4+10134t3−395t2−108t−4,(t↦tlog⁡(−72277241424336888589729529t636780392702955027644+2549382420526595647929629t518390196351477513822+31182985334944362544409t415763025444123583276−437989287638021185973565t318390196351477513822−27613275754890251531439t218390196351477513822+25709295147507149852993t110341178108865082932+x+92542818888290089965755170589054432541466)))\int \frac{\left(3 x^{2} + x\right) - 2}{\left(- x^{2} + \left(2 x^{7} + 3 x^{5}\right)\right) - 1}\, dx = C + 3 \operatorname{RootSum} {\left(6219033 t^{7} - 145850 t^{5} - 2622 t^{4} + 1213 t^{3} - 85 t^{2} + 18 t - 1, \left( t \mapsto t \log{\left(- \frac{1338254223722234609519895 t^{6}}{614170995658912774} - \frac{141607889991322281135329 t^{5}}{614170995658912774} + \frac{16779000163258668460573 t^{4}}{614170995658912774} + \frac{7121143425189507540611 t^{3}}{1842512986976738322} - \frac{79086989811432346138 t^{2}}{921256493488369161} + \frac{39993172691320168133 t}{1842512986976738322} + x - \frac{5978319999868176713}{1842512986976738322} \right)} \right)\right)} + \operatorname{RootSum} {\left(6219033 t^{7} + 86245 t^{5} - 25115 t^{4} + 5155 t^{3} - 551 t^{2} + 42 t - 2, \left( t \mapsto t \log{\left(- \frac{158367799939777137068438427 t^{6}}{777313771685400160162} - \frac{3208271250789907217809437 t^{5}}{388656885842700080081} - \frac{4118014325496337342677133 t^{4}}{777313771685400160162} + \frac{282755219073426871910893 t^{3}}{777313771685400160162} - \frac{121941987059033803462821 t^{2}}{777313771685400160162} + \frac{14998806734791161779739 t}{777313771685400160162} + x - \frac{458764957683141536262}{388656885842700080081} \right)} \right)\right)} - 2 \operatorname{RootSum} {\left(6219033 t^{7} - 35009 t^{5} + 74300 t^{4} + 10134 t^{3} - 395 t^{2} - 108 t - 4, \left( t \mapsto t \log{\left(- \frac{72277241424336888589729529 t^{6}}{36780392702955027644} + \frac{2549382420526595647929629 t^{5}}{18390196351477513822} + \frac{31182985334944362544409 t^{4}}{15763025444123583276} - \frac{437989287638021185973565 t^{3}}{18390196351477513822} - \frac{27613275754890251531439 t^{2}}{18390196351477513822} + \frac{25709295147507149852993 t}{110341178108865082932} + x + \frac{925428188882900899657}{55170589054432541466} \right)} \right)\right)}
Simplificar
Gráfica
1.00001.01001.00101.00201.00301.00401.00501.00601.00701.00801.00901.0-1.0
Trazar el gráfico f(x)
Respuesta [src] 
 oo                         
  /                         
 |                          
 |                  2       
 |      -2 + x + 3*x        
 |  --------------------- dx
 |        2      7      5   
 |  -1 - x  + 2*x  + 3*x    
 |                          
/                           
1
∫1∞3x2+x−22x7+3x5−x2−1 dx\int\limits_{1}^{\infty} \frac{3 x^{2} + x - 2}{2 x^{7} + 3 x^{5} - x^{2} - 1}\, dx 
=
= 
 oo                         
  /                         
 |                          
 |                  2       
 |      -2 + x + 3*x        
 |  --------------------- dx
 |        2      7      5   
 |  -1 - x  + 2*x  + 3*x    
 |                          
/                           
1
∫1∞3x2+x−22x7+3x5−x2−1 dx\int\limits_{1}^{\infty} \frac{3 x^{2} + x - 2}{2 x^{7} + 3 x^{5} - x^{2} - 1}\, dx 
Integral((-2 + x + 3*x^2)/(-1 - x^2 + 2*x^7 + 3*x^5), (x, 1, oo))

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

    © Sr Examen – Калькулятор