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Integral de x^13/(x^5+x^3+1)^2 dx
Solución
Ha introducido
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oo / | | 13 | x | -------------- dx | 2 | / 5 3 \ | \x + x + 1/ | / 0
$$\int\limits_{0}^{\infty} \frac{x^{13}}{\left(\left(x^{5} + x^{3}\right) + 1\right)^{2}}\, dx$$
Integral(x^13/(x^5 + x^3 + 1)^2, (x, 0, oo))
Respuesta (Indefinida)
[src]
/ | | 13 / / 2 3 4\\ / / 4 3 2\\ / / 3 2 4\\ / / 2 3 4\\ / / 3 2 4 \\ / / 3 2 4\\ / / 3 4 2 \\ 4 3 2 4 2 4 3 / 4 3 2\ / 2 4 3\ / / 4 3 2\\ / / 2 3 4\\ | x 2 | 5 3 2 | 13 2*t 2918*t 3233*t 22631*t || | 5 3 2 | 2536678726146920768009914566 51415602083482733676020730820237*t 874911410055162894534919988675*t 57799106089266511847971052385*t 238165824682266762776982753785*t || | 5 3 2 |290332708249646050 153545298040762276407875*t 904637403823710720545*t 8373100771536560567*t 73508719629038995551746147*t || | 5 3 2 | 4255200 62335027*t 105468750*t 478209195*t 6096225625*t || | 5 3 2 | 958304371714520226706258 868196506949216703376421237*t 502435466831356689591754543*t 333030732113469856273732750*t 58541432542729362533762198*t|| | 5 4 3 2 |475 100223*t 6875*t 12743*t 113155*t || | 5 3 2 | 1395450 1277439125*t 187442874*t 52536215*t 19763162*t|| x -60 - 661*x - 36*x + 100*x + 250*x -36 + 60*x + 150*x + 250*x + 625*x 2*\250 + 36*x + 60*x + 150*x + 661*x / 3*\625 + 36*x + 90*x + 150*x + 375*x / | 5 3 2 | 2959556 2728580874*t 43205812*t 55949997*t 124306844*t || | 5 3 2 |290332708249646050 180927480764742144109*t 8373100771536560567*t 1228362384326098211263*t 73508719629038995551746147*t || | -------------- dx = C - x - RootSum|3233*t - 45*t + 5*t + 5*t - 1, t -> t*log|--- + x - --- + ------- + ------- + --------|| - RootSum|33792250337*t - 1157772780*t - 66179744*t + 33414720*t - 3242336, t -> t*log|- ---------------------------- + x - ----------------------------------- - --------------------------------- + ------------------------------- + ---------------------------------|| - 3*RootSum|33792250337*t - 110920500*t - 1336176*t + 324000*t + 7776, t -> t*log|------------------ + x - --------------------------- - ------------------------ + --------------------- + -----------------------------|| - 2*RootSum|3233*t + 27*t - 50*t + 1, t -> t*log|- ------- + x - ---------- + ------------ + ------------ + -------------|| - 2*RootSum|33792250337*t + 609322167*t + 25541028*t + 815184*t + 763263, t -> t*log|- ------------------------- + x - ------------------------------ - ------------------------------ - ------------------------------ - ----------------------------|| + 3*RootSum|3233*t - 3233*t + 1277*t - 250*t + 25*t - 1, t -> t*log|--- + x - --------- - ------ + -------- + ---------|| + 4*RootSum|3233*t + 75*t + 4*t + 1, t -> t*log|- ------- + x - ------------- - ------------ - ----------- - ----------|| + -- + ------------------------------------- + ------------------------------------- - ---------------------------------------- + ---------------------------------------- + RootSum|3233*t - 125*t - 4*t + 4*t - 1, t -> t*log|- -------- + x - ------------- - ----------- + ---------- + ------------|| + RootSum|33792250337*t - 308112500*t + 6186000*t + 2500000*t - 100000, t -> t*log|------------------ + x - ------------------------ - --------------------- + ------------------------- + -----------------------------|| | 2 \ \125 25 125 125 125 // \ \ 3051877583154404909829226613 48830041330470478557267625808 24415020665235239278633812904 6103755166308809819658453226 6103755166308809819658453226 // \ \280175042313434077 30258904569850880316 5043150761641813386 840525126940302231 363106854838210563792 // \ \ 7363759 7363759 7363759 7363759 7363759 // \ \ 2299388666307718707816583 1171386679062422737944297 20694497996769468370349247 390462226354140912648099 6898165998923156123449749 // \ \ 81 81 81 27 81 // \ \ 9712831 9712831 9712831 9712831 9712831 // 4 3 5 3 5 3 5 3 5 \ \ 10177721 10177721 10177721 10177721 10177721 // \ \280175042313434077 2801750423134340770 1400875211567170385 1120700169253736308 2801750423134340770000 // | / 5 3 \ 3233 + 3233*x + 3233*x 3233 + 3233*x + 3233*x 3233 + 3233*x + 3233*x 3233 + 3233*x + 3233*x | \x + x + 1/ | /
$$\int \frac{x^{13}}{\left(\left(x^{5} + x^{3}\right) + 1\right)^{2}}\, dx = C + \frac{x^{4}}{4} - x^{2} - 2 \operatorname{RootSum} {\left(3233 t^{5} + 27 t^{3} - 50 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{6096225625 t^{4}}{7363759} + \frac{478209195 t^{3}}{7363759} + \frac{105468750 t^{2}}{7363759} - \frac{62335027 t}{7363759} + x - \frac{4255200}{7363759} \right)} \right)\right)} + 4 \operatorname{RootSum} {\left(3233 t^{5} + 75 t^{3} + 4 t^{2} + 1, \left( t \mapsto t \log{\left(- \frac{187442874 t^{4}}{9712831} - \frac{1277439125 t^{3}}{9712831} - \frac{52536215 t^{2}}{9712831} - \frac{19763162 t}{9712831} + x - \frac{1395450}{9712831} \right)} \right)\right)} - \operatorname{RootSum} {\left(3233 t^{5} - 45 t^{3} + 5 t^{2} + 5 t - 1, \left( t \mapsto t \log{\left(\frac{22631 t^{4}}{125} + \frac{3233 t^{3}}{125} + \frac{2918 t^{2}}{125} - \frac{2 t}{25} + x + \frac{13}{125} \right)} \right)\right)} + \operatorname{RootSum} {\left(3233 t^{5} - 125 t^{3} - 4 t^{2} + 4 t - 1, \left( t \mapsto t \log{\left(- \frac{2728580874 t^{4}}{10177721} - \frac{43205812 t^{3}}{10177721} + \frac{124306844 t^{2}}{10177721} + \frac{55949997 t}{10177721} + x - \frac{2959556}{10177721} \right)} \right)\right)} - 3 \operatorname{RootSum} {\left(33792250337 t^{5} - 110920500 t^{3} - 1336176 t^{2} + 324000 t + 7776, \left( t \mapsto t \log{\left(\frac{73508719629038995551746147 t^{4}}{363106854838210563792} - \frac{153545298040762276407875 t^{3}}{30258904569850880316} - \frac{904637403823710720545 t^{2}}{5043150761641813386} + \frac{8373100771536560567 t}{840525126940302231} + x + \frac{290332708249646050}{280175042313434077} \right)} \right)\right)} + \operatorname{RootSum} {\left(33792250337 t^{5} - 308112500 t^{3} + 6186000 t^{2} + 2500000 t - 100000, \left( t \mapsto t \log{\left(\frac{73508719629038995551746147 t^{4}}{2801750423134340770000} + \frac{1228362384326098211263 t^{3}}{1120700169253736308} - \frac{180927480764742144109 t^{2}}{2801750423134340770} - \frac{8373100771536560567 t}{1400875211567170385} + x + \frac{290332708249646050}{280175042313434077} \right)} \right)\right)} - 2 \operatorname{RootSum} {\left(33792250337 t^{5} + 609322167 t^{3} + 25541028 t^{2} + 815184 t + 763263, \left( t \mapsto t \log{\left(- \frac{333030732113469856273732750 t^{4}}{390462226354140912648099} - \frac{868196506949216703376421237 t^{3}}{1171386679062422737944297} - \frac{502435466831356689591754543 t^{2}}{20694497996769468370349247} - \frac{58541432542729362533762198 t}{6898165998923156123449749} + x - \frac{958304371714520226706258}{2299388666307718707816583} \right)} \right)\right)} - \operatorname{RootSum} {\left(33792250337 t^{5} - 1157772780 t^{3} - 66179744 t^{2} + 33414720 t - 3242336, \left( t \mapsto t \log{\left(- \frac{51415602083482733676020730820237 t^{4}}{48830041330470478557267625808} - \frac{874911410055162894534919988675 t^{3}}{24415020665235239278633812904} + \frac{238165824682266762776982753785 t^{2}}{6103755166308809819658453226} + \frac{57799106089266511847971052385 t}{6103755166308809819658453226} + x - \frac{2536678726146920768009914566}{3051877583154404909829226613} \right)} \right)\right)} + 3 \operatorname{RootSum} {\left(3233 t^{5} - 3233 t^{4} + 1277 t^{3} - 250 t^{2} + 25 t - 1, \left( t \mapsto t \log{\left(\frac{113155 t^{4}}{81} - \frac{100223 t^{3}}{81} + \frac{12743 t^{2}}{27} - \frac{6875 t}{81} + x + \frac{475}{81} \right)} \right)\right)} - \frac{2 \left(36 x^{4} + 150 x^{3} + 661 x^{2} + 60 x + 250\right)}{3233 x^{5} + 3233 x^{3} + 3233} + \frac{3 \left(90 x^{4} + 375 x^{3} + 36 x^{2} + 150 x + 625\right)}{3233 x^{5} + 3233 x^{3} + 3233} + \frac{150 x^{4} + 625 x^{3} + 60 x^{2} + 250 x - 36}{3233 x^{5} + 3233 x^{3} + 3233} + \frac{250 x^{4} - 36 x^{3} + 100 x^{2} - 661 x - 60}{3233 x^{5} + 3233 x^{3} + 3233}$$
Gráfica
Respuesta
[src]
oo / | | 13 | x | -------------- dx | 2 | / 3 5\ | \1 + x + x / | / 0
$$\int\limits_{0}^{\infty} \frac{x^{13}}{\left(x^{5} + x^{3} + 1\right)^{2}}\, dx$$
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oo / | | 13 | x | -------------- dx | 2 | / 3 5\ | \1 + x + x / | / 0
$$\int\limits_{0}^{\infty} \frac{x^{13}}{\left(x^{5} + x^{3} + 1\right)^{2}}\, dx$$
Integral(x^13/(1 + x^3 + x^5)^2, (x, 0, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.