1 / | | 1 | -------- dx | 2 | 7*x - 8 | / 0
Integral(1/(7*x^2 - 8), (x, 0, 1))
PieceweseRule(subfunctions=[(ArctanRule(a=1, b=7, c=-8, context=1/(7*x**2 - 8), symbol=x), False), (ArccothRule(a=1, b=7, c=-8, context=1/(7*x**2 - 8), symbol=x), x**2 > 8/7), (ArctanhRule(a=1, b=7, c=-8, context=1/(7*x**2 - 8), symbol=x), x**2 < 8/7)], context=1/(7*x**2 - 8), symbol=x)
Añadimos la constante de integración:
Respuesta:
// / ____\ \ || ____ |x*\/ 14 | | ||-\/ 14 *acoth|--------| | / || \ 4 / 2 | | ||------------------------ for x > 8/7| | 1 || 28 | | -------- dx = C + |< | | 2 || / ____\ | | 7*x - 8 || ____ |x*\/ 14 | | | ||-\/ 14 *atanh|--------| | / || \ 4 / 2 | ||------------------------ for x < 8/7| \\ 28 /
/ / ____\\ / ____\ / / ____\\ / ____\ ____ | |2*\/ 14 || ____ | 2*\/ 14 | ____ | | 2*\/ 14 || ____ |2*\/ 14 | \/ 14 *|pi*I + log|--------|| \/ 14 *log|1 + --------| \/ 14 *|pi*I + log|-1 + --------|| \/ 14 *log|--------| \ \ 7 // \ 7 / \ \ 7 // \ 7 / - ----------------------------- - ------------------------ + ---------------------------------- + -------------------- 56 56 56 56
=
/ / ____\\ / ____\ / / ____\\ / ____\ ____ | |2*\/ 14 || ____ | 2*\/ 14 | ____ | | 2*\/ 14 || ____ |2*\/ 14 | \/ 14 *|pi*I + log|--------|| \/ 14 *log|1 + --------| \/ 14 *|pi*I + log|-1 + --------|| \/ 14 *log|--------| \ \ 7 // \ 7 / \ \ 7 // \ 7 / - ----------------------------- - ------------------------ + ---------------------------------- + -------------------- 56 56 56 56
-sqrt(14)*(pi*i + log(2*sqrt(14)/7))/56 - sqrt(14)*log(1 + 2*sqrt(14)/7)/56 + sqrt(14)*(pi*i + log(-1 + 2*sqrt(14)/7))/56 + sqrt(14)*log(2*sqrt(14)/7)/56
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.