0 / | | 1 | ------------- dx | 2 | 1 + 4*cos (x) | / pi -- 4
Integral(1/(1 + 4*cos(x)^2), (x, pi/4, 0))
/ /x pi\ \ / /x pi\ \ | |- - --| | | |- - --| | / ___ | |2 2 | / ___ /x\\| ___ | |2 2 | / ___ /x\\| | \/ 5 *|pi*floor|------| + atan|-2 + \/ 5 *tan|-||| \/ 5 *|pi*floor|------| + atan|2 + \/ 5 *tan|-||| | 1 \ \ pi / \ \2/// \ \ pi / \ \2/// | ------------- dx = C + -------------------------------------------------- + ------------------------------------------------- | 2 5 5 | 1 + 4*cos (x) | /
___ / / ___ / ___\\\ ___ / / ___ / ___\\\ ___ ___ \/ 5 *\-pi - atan\2 - \/ 5 *\-1 + \/ 2 /// \/ 5 *\-pi + atan\2 + \/ 5 *\-1 + \/ 2 /// \/ 5 *(-pi - atan(2)) \/ 5 *(-pi + atan(2)) - ------------------------------------------ - ------------------------------------------ + --------------------- + --------------------- 5 5 5 5
=
___ / / ___ / ___\\\ ___ / / ___ / ___\\\ ___ ___ \/ 5 *\-pi - atan\2 - \/ 5 *\-1 + \/ 2 /// \/ 5 *\-pi + atan\2 + \/ 5 *\-1 + \/ 2 /// \/ 5 *(-pi - atan(2)) \/ 5 *(-pi + atan(2)) - ------------------------------------------ - ------------------------------------------ + --------------------- + --------------------- 5 5 5 5
-sqrt(5)*(-pi - atan(2 - sqrt(5)*(-1 + sqrt(2))))/5 - sqrt(5)*(-pi + atan(2 + sqrt(5)*(-1 + sqrt(2))))/5 + sqrt(5)*(-pi - atan(2))/5 + sqrt(5)*(-pi + atan(2))/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.