oo / | | 3*x + 1 | ------------------- dx | 4 3 | x + 2*x + 7*x + 8 | / 1
Integral((3*x + 1)/(x^4 + 2*x^3 + 7*x + 8), (x, 1, oo))
/ 2\ | / ____________________ \ | | | / _____ | | | | / 1 227*\/ 633 4 | | | 15192*|3 / ---- + ----------- - ------------------------------| | | ____________________ |\/ 3798 21637206 ____________________| | | / _____ | / _____ | | / ____________________ \ | / 1 227*\/ 633 | / 1 227*\/ 633 | | | / _____ | | 5697*3 / ---- + ----------- | 5697*3 / ---- + ----------- | | | / 1 227*\/ 633 4 | | 97 4 \/ 3798 21637206 \ \/ 3798 21637206 / | 25*|3 / ---- + ----------- - ------------------------------|*log|--- + x - ----------------------------- + ------------------------------ + -------------------------------------------------------------------| |\/ 3798 21637206 ____________________| |227 ____________________ 227 227 | / / 2\\ | / _____ | | / _____ | / | 3 2 |9272 58869*t 87354*t || | / 1 227*\/ 633 | | / 1 227*\/ 633 | | 2*RootSum|1899*t - 1899*t + 607*t - 64, t -> t*log|---- + x - ------- + --------|| | 5697*3 / ---- + ----------- | | 227*3 / ---- + ----------- | | 3*x + 1 2*log(1 + x) \ \457 457 457 // \ \/ 3798 21637206 / \ \/ 3798 21637206 / | ------------------- dx = C - ------------ + ------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 4 3 9 9 9 | x + 2*x + 7*x + 8 | /
oo / | | 1 + 3*x | ------------------- dx | 4 3 | 8 + x + 2*x + 7*x | / 1
=
oo / | | 1 + 3*x | ------------------- dx | 4 3 | 8 + x + 2*x + 7*x | / 1
Integral((1 + 3*x)/(8 + x^4 + 2*x^3 + 7*x), (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.