Integral de 1/(5+4cosx)^2 dx
Solución
Respuesta (Indefinida)
[src]
/ /x pi\ / /x\\\ / /x pi\ / /x\\\
| |- - --| |tan|-||| | |- - --| |tan|-|||
/ /x\ | |2 2 | | \2/|| 2/x\ | |2 2 | | \2/||
| 24*tan|-| 90*|pi*floor|------| + atan|------|| 10*tan |-|*|pi*floor|------| + atan|------||
| 1 \2/ \ \ pi / \ 3 // \2/ \ \ pi / \ 3 //
| --------------- dx = C - ---------------- + ------------------------------------ + --------------------------------------------
| 2 2/x\ 2/x\ 2/x\
| (5 + 4*cos(x)) 243 + 27*tan |-| 243 + 27*tan |-| 243 + 27*tan |-|
| \2/ \2/ \2/
/
∫(4cos(x)+5)21dx=C+27tan2(2x)+24310(atan(3tan(2x))+π⌊π2x−2π⌋)tan2(2x)+27tan2(2x)+24390(atan(3tan(2x))+π⌊π2x−2π⌋)−27tan2(2x)+24324tan(2x)
Gráfica
/ /tan(1/2)\\ 2 / /tan(1/2)\\
90*|-pi + atan|--------|| 10*tan (1/2)*|-pi + atan|--------||
10*pi 24*tan(1/2) \ \ 3 // \ \ 3 //
----- - ------------------ + ------------------------- + -----------------------------------
27 2 2 2
243 + 27*tan (1/2) 243 + 27*tan (1/2) 243 + 27*tan (1/2)
27tan2(21)+24390(−π+atan(3tan(21)))−27tan2(21)+24324tan(21)+27tan2(21)+24310(−π+atan(3tan(21)))tan2(21)+2710π
=
/ /tan(1/2)\\ 2 / /tan(1/2)\\
90*|-pi + atan|--------|| 10*tan (1/2)*|-pi + atan|--------||
10*pi 24*tan(1/2) \ \ 3 // \ \ 3 //
----- - ------------------ + ------------------------- + -----------------------------------
27 2 2 2
243 + 27*tan (1/2) 243 + 27*tan (1/2) 243 + 27*tan (1/2)
27tan2(21)+24390(−π+atan(3tan(21)))−27tan2(21)+24324tan(21)+27tan2(21)+24310(−π+atan(3tan(21)))tan2(21)+2710π
10*pi/27 - 24*tan(1/2)/(243 + 27*tan(1/2)^2) + 90*(-pi + atan(tan(1/2)/3))/(243 + 27*tan(1/2)^2) + 10*tan(1/2)^2*(-pi + atan(tan(1/2)/3))/(243 + 27*tan(1/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.