Sr Examen
Integral de sqrt(x)/(1+x^7) dx
Solución
Ha introducido
[src]
oo / | | ___ | \/ x | ------ dx | 7 | 1 + x | / 1
$$\int\limits_{1}^{\infty} \frac{\sqrt{x}}{x^{7} + 1}\, dx$$
Integral(sqrt(x)/(1 + x^7), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / / 3 5 7 9 11\\ / / 11 7 3 5 9\\ / / 7 3 5 9 11\\ / / 5 3 7 9 11\\ / / 3 5 7 9 11\\ / / 9 5 3 7 11\\ | | 12 10 8 6 4 2 | ___ 11102*t 2708328*t 283817408*t 15827084672*t 20661046784*t 10578455953408*t || | 12 8 6 4 2 | ___ 2851224456192*t 1054135040*t 91238*t 756*t 6818840*t 3689472640*t || | 12 6 4 2 | ___ 102589928*t 5103*t 187278*t 12917380*t 4611840800*t 2629118203264*t || | 12 6 4 2 | ___ 192080*t 2821*t 41846*t 103531120*t 5534208960*t 134296804096*t || | 12 10 8 6 4 2 | ___ 3696*t 3715376*t 551653760*t 54950553728*t 100353655808*t 70164914878464*t || | 12 8 6 4 2 | ___ 4427367168*t 2055256*t 581*t 41846*t 173179328*t 185949421056*t || | ___ 8*RootSum|1157018619904*t + 41322093568*t + 632481024*t + 5378240*t + 38416*t - 196*t + 1, t -> t*log|\/ x + ------- + ---------- + ------------ + -------------- + -------------- + ------------------|| 4*RootSum|1157018619904*t + 421654016*t - 2151296*t + 38416*t + 392*t + 1, t -> t*log|\/ x - ----------------- - ------------- - -------- - ----- + ---------- + -------------|| / ___\ 2*RootSum|1157018619904*t + 5378240*t + 76832*t + 196*t + 1, t -> t*log|\/ x - ------------ + ------ + --------- + ----------- + ------------- + -----------------|| 2*RootSum|1157018619904*t + 5378240*t + 76832*t + 196*t + 1, t -> t*log|\/ x - --------- + ------ + -------- + ------------ + ------------- + ----------------|| 6*RootSum|1157018619904*t + 41322093568*t + 632481024*t + 5378240*t + 38416*t - 196*t + 1, t -> t*log|\/ x - ------ + ---------- + ------------ + -------------- + --------------- + ------------------|| 10*RootSum|1157018619904*t + 421654016*t - 2151296*t + 38416*t + 392*t + 1, t -> t*log|\/ x - ------------- - ---------- - ----- + -------- + ------------ + ----------------|| | \/ x \ \ 1247 1247 1247 1247 43 1247 // \ \ 29 29 29 29 29 29 // 2*atan\\/ x / \ \ 43 344 43 43 43 43 // \ \ 43 172 43 43 43 43 // \ \ 1247 1247 1247 1247 43 1247 // \ \ 29 29 58 29 29 29 // | ------ dx = C - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 7 7 7 7 7 7 7 7 | 1 + x | /
$$\int \frac{\sqrt{x}}{x^{7} + 1}\, dx = C - \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{7} + \frac{2 \operatorname{RootSum} {\left(1157018619904 t^{12} + 5378240 t^{6} + 76832 t^{4} + 196 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{134296804096 t^{11}}{43} + \frac{5534208960 t^{9}}{43} + \frac{103531120 t^{7}}{43} - \frac{192080 t^{5}}{43} + \frac{41846 t^{3}}{43} + \frac{2821 t}{172} + \sqrt{x} \right)} \right)\right)}}{7} + \frac{2 \operatorname{RootSum} {\left(1157018619904 t^{12} + 5378240 t^{6} + 76832 t^{4} + 196 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{2629118203264 t^{11}}{43} + \frac{4611840800 t^{9}}{43} - \frac{102589928 t^{7}}{43} + \frac{12917380 t^{5}}{43} + \frac{187278 t^{3}}{43} + \frac{5103 t}{344} + \sqrt{x} \right)} \right)\right)}}{7} - \frac{4 \operatorname{RootSum} {\left(1157018619904 t^{12} + 421654016 t^{8} - 2151296 t^{6} + 38416 t^{4} + 392 t^{2} + 1, \left( t \mapsto t \log{\left(- \frac{2851224456192 t^{11}}{29} + \frac{3689472640 t^{9}}{29} - \frac{1054135040 t^{7}}{29} + \frac{6818840 t^{5}}{29} - \frac{91238 t^{3}}{29} - \frac{756 t}{29} + \sqrt{x} \right)} \right)\right)}}{7} + \frac{10 \operatorname{RootSum} {\left(1157018619904 t^{12} + 421654016 t^{8} - 2151296 t^{6} + 38416 t^{4} + 392 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{185949421056 t^{11}}{29} - \frac{4427367168 t^{9}}{29} + \frac{173179328 t^{7}}{29} - \frac{2055256 t^{5}}{29} + \frac{41846 t^{3}}{29} - \frac{581 t}{58} + \sqrt{x} \right)} \right)\right)}}{7} + \frac{6 \operatorname{RootSum} {\left(1157018619904 t^{12} + 41322093568 t^{10} + 632481024 t^{8} + 5378240 t^{6} + 38416 t^{4} - 196 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{70164914878464 t^{11}}{1247} + \frac{100353655808 t^{9}}{43} + \frac{54950553728 t^{7}}{1247} + \frac{551653760 t^{5}}{1247} + \frac{3715376 t^{3}}{1247} - \frac{3696 t}{1247} + \sqrt{x} \right)} \right)\right)}}{7} - \frac{8 \operatorname{RootSum} {\left(1157018619904 t^{12} + 41322093568 t^{10} + 632481024 t^{8} + 5378240 t^{6} + 38416 t^{4} - 196 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{10578455953408 t^{11}}{1247} + \frac{20661046784 t^{9}}{43} + \frac{15827084672 t^{7}}{1247} + \frac{283817408 t^{5}}{1247} + \frac{2708328 t^{3}}{1247} + \frac{11102 t}{1247} + \sqrt{x} \right)} \right)\right)}}{7}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.