Sr Examen
Integral de (7x^2+x-(arctg(8x)^2))/(2x^7-x^3+4) dx
Solución
Ha introducido
[src]
oo / | | 2 2 | 7*x + x - atan (8*x) | --------------------- dx | 7 3 | 2*x - x + 4 | / 1
$$\int\limits_{1}^{\infty} \frac{\left(7 x^{2} + x\right) - \operatorname{atan}^{2}{\left(8 x \right)}}{\left(2 x^{7} - x^{3}\right) + 4}\, dx$$
Integral((7*x^2 + x - atan(8*x)^2)/(2*x^7 - x^3 + 4), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | 2 2 | 2 / / 2 3 4 5 6\\ / / 3 2 6 5 4\\ | 7*x + x - atan (8*x) | atan (8*x) | 7 5 4 3 2 | 51 95*t 11*t 24*t 216*t 210826144*t 1264956864*t || | 7 5 4 3 | 35017530913884562344 6670024174736842976*t 38892520282129683769440*t 144135058974998369220236*t 8931606587684877249221120*t 46634544318935136053174272*t 175786210992577898590665984*t || | --------------------- dx = C - | ------------- dx + 7*RootSum|1686609152*t + 2016*t - 112*t - 203*t + 21*t + 7*t - 1, t -> t*log|--- + x - ----- - ---- + ----- + ------ + ------------ + -------------|| + RootSum|3373218304*t + 4302592*t - 128*t + 2156*t + 1, t -> t*log|--------------------- + x + --------------------- + -------------------------- + --------------------------- + ---------------------------- + ----------------------------- + ------------------------------|| | 7 3 | 3 7 \ \392 28 56 7 7 49 49 // \ \571960101912267146293 571960101912267146293 571960101912267146293 571960101912267146293 571960101912267146293 571960101912267146293 571960101912267146293 // | 2*x - x + 4 | 4 - x + 2*x | | / /
$$\int \frac{\left(7 x^{2} + x\right) - \operatorname{atan}^{2}{\left(8 x \right)}}{\left(2 x^{7} - x^{3}\right) + 4}\, dx = C - \int \frac{\operatorname{atan}^{2}{\left(8 x \right)}}{2 x^{7} - x^{3} + 4}\, dx + \operatorname{RootSum} {\left(3373218304 t^{7} + 4302592 t^{5} - 128 t^{4} + 2156 t^{3} + 1, \left( t \mapsto t \log{\left(\frac{8931606587684877249221120 t^{6}}{571960101912267146293} + \frac{46634544318935136053174272 t^{5}}{571960101912267146293} + \frac{175786210992577898590665984 t^{4}}{571960101912267146293} + \frac{38892520282129683769440 t^{3}}{571960101912267146293} + \frac{144135058974998369220236 t^{2}}{571960101912267146293} + \frac{6670024174736842976 t}{571960101912267146293} + x + \frac{35017530913884562344}{571960101912267146293} \right)} \right)\right)} + 7 \operatorname{RootSum} {\left(1686609152 t^{7} + 2016 t^{5} - 112 t^{4} - 203 t^{3} + 21 t^{2} + 7 t - 1, \left( t \mapsto t \log{\left(\frac{1264956864 t^{6}}{49} + \frac{210826144 t^{5}}{49} + \frac{216 t^{4}}{7} + \frac{24 t^{3}}{7} - \frac{95 t^{2}}{28} - \frac{11 t}{56} + x + \frac{51}{392} \right)} \right)\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.