Sr Examen
Integral de (x-8)/(x^3+2*x-x^-2+4) dx
Solución
Ha introducido
[src]
1 / | | x - 8 | ----------------- dx | 3 1 | x + 2*x - -- + 4 | 2 | x | / 0
$$\int\limits_{0}^{1} \frac{x - 8}{\left(\left(x^{3} + 2 x\right) - \frac{1}{x^{2}}\right) + 4}\, dx$$
Integral((x - 8)/(x^3 + 2*x - 1/x^2 + 4), (x, 0, 1))
Respuesta
[src]
/ / 2 3 4 \\ / / 2 3 4 \\
| 4 3 2 |21895746448 117779837164*t 39834536324*t 46625933211*t 196049590526*t|| | 4 3 2 |75533431269 117779837164*t 39834536324*t 46625933211*t 196049590526*t||
- RootSum|3267*t - 9801*t + 7623*t - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------|| - 3*log(2) + RootSum|3267*t - 9801*t + 7623*t - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------||
\ \53637684821 22987579209 53637684821 53637684821 160913054463 // \ \53637684821 22987579209 53637684821 53637684821 160913054463 //
$$- \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{21895746448}{53637684821} \right)} \right)\right)} + \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{75533431269}{53637684821} \right)} \right)\right)} - 3 \log{\left(2 \right)}$$
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/ / 2 3 4 \\ / / 2 3 4 \\
| 4 3 2 |21895746448 117779837164*t 39834536324*t 46625933211*t 196049590526*t|| | 4 3 2 |75533431269 117779837164*t 39834536324*t 46625933211*t 196049590526*t||
- RootSum|3267*t - 9801*t + 7623*t - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------|| - 3*log(2) + RootSum|3267*t - 9801*t + 7623*t - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------||
\ \53637684821 22987579209 53637684821 53637684821 160913054463 // \ \53637684821 22987579209 53637684821 53637684821 160913054463 //
$$- \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{21895746448}{53637684821} \right)} \right)\right)} + \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{75533431269}{53637684821} \right)} \right)\right)} - 3 \log{\left(2 \right)}$$
-RootSum(3267*_t^4 - 9801*_t^3 + 7623*_t^2 - 841*_t - 1261, Lambda(_t, _t*log(21895746448/53637684821 - 117779837164*_t^2/22987579209 + 39834536324*_t^3/53637684821 + 46625933211*_t^4/53637684821 + 196049590526*_t/160913054463))) - 3*log(2) + RootSum(3267*_t^4 - 9801*_t^3 + 7623*_t^2 - 841*_t - 1261, Lambda(_t, _t*log(75533431269/53637684821 - 117779837164*_t^2/22987579209 + 39834536324*_t^3/53637684821 + 46625933211*_t^4/53637684821 + 196049590526*_t/160913054463)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.