Sr Examen
Integral de (x^8-1)/(x^10+1) dx
Solución
Ha introducido
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1 / | | 8 | x - 1 | ------- dx | 10 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x^{8} - 1}{x^{10} + 1}\, dx$$
Integral((x^8 - 1)/(x^10 + 1), (x, 0, 1))
Respuesta (Indefinida)
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/ | | 8 / / 5 3 7\\ / / 7 5 3 \\ / / 7 3 5\\ / / 3 5 7\\ | x - 1 | 8 4 2 | 80000*t 120*t 5800*t 5600000*t || | 8 6 4 | 2800000*t 240000*t 5400*t 20*t|| | 8 4 2 | 400000*t 1200*t 70*t 100000*t || | 8 6 4 | 2400*t 70*t 40000*t 1200000*t || | ------- dx = C - RootSum|4000000*t + 4000*t + 100*t + 1, t -> t*log|x - -------- + ----- + ------- + ----------|| - RootSum|4000000*t + 200000*t + 4000*t + 1, t -> t*log|x - ---------- - --------- - ------- - ----|| + RootSum|4000000*t + 4000*t + 100*t + 1, t -> t*log|x - --------- - ------- + ---- + ---------|| + RootSum|4000000*t + 200000*t + 4000*t + 1, t -> t*log|x - ------- - ---- + -------- + ----------|| | 10 \ \ 11 11 11 11 // \ \ 11 11 11 11 // \ \ 11 11 11 11 // \ \ 11 11 11 11 // | x + 1 | /
$$\int \frac{x^{8} - 1}{x^{10} + 1}\, dx = C + \operatorname{RootSum} {\left(4000000 t^{8} + 4000 t^{4} + 100 t^{2} + 1, \left( t \mapsto t \log{\left(- \frac{400000 t^{7}}{11} + \frac{100000 t^{5}}{11} - \frac{1200 t^{3}}{11} + \frac{70 t}{11} + x \right)} \right)\right)} - \operatorname{RootSum} {\left(4000000 t^{8} + 200000 t^{6} + 4000 t^{4} + 1, \left( t \mapsto t \log{\left(- \frac{2800000 t^{7}}{11} - \frac{240000 t^{5}}{11} - \frac{5400 t^{3}}{11} - \frac{20 t}{11} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(4000000 t^{8} + 200000 t^{6} + 4000 t^{4} + 1, \left( t \mapsto t \log{\left(\frac{1200000 t^{7}}{11} + \frac{40000 t^{5}}{11} - \frac{2400 t^{3}}{11} - \frac{70 t}{11} + x \right)} \right)\right)} - \operatorname{RootSum} {\left(4000000 t^{8} + 4000 t^{4} + 100 t^{2} + 1, \left( t \mapsto t \log{\left(\frac{5600000 t^{7}}{11} - \frac{80000 t^{5}}{11} + \frac{5800 t^{3}}{11} + \frac{120 t}{11} + x \right)} \right)\right)}$$
Gráfica
Respuesta
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/ 4 2 \ RootSum\2000*t - 100*t + 1, t -> t*log(2 - 10*t)/
$$\operatorname{RootSum} {\left(2000 t^{4} - 100 t^{2} + 1, \left( t \mapsto t \log{\left(2 - 10 t \right)} \right)\right)}$$
=
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/ 4 2 \ RootSum\2000*t - 100*t + 1, t -> t*log(2 - 10*t)/
$$\operatorname{RootSum} {\left(2000 t^{4} - 100 t^{2} + 1, \left( t \mapsto t \log{\left(2 - 10 t \right)} \right)\right)}$$
RootSum(2000*_t^4 - 100*_t^2 + 1, Lambda(_t, _t*log(2 - 10*_t)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.