Integral de 1/(1+4cosx) dx
Solución
Respuesta (Indefinida)
[src]
/ ____ \ / ____ \
/ ____ | \/ 15 /x\| ____ |\/ 15 /x\|
| \/ 15 *log|- ------ + tan|-|| \/ 15 *log|------ + tan|-||
| 1 \ 3 \2// \ 3 \2//
| ------------ dx = C - ----------------------------- + ---------------------------
| 1 + 4*cos(x) 15 15
|
/
∫4cos(x)+11dx=C−1515log(tan(2x)−315)+1515log(tan(2x)+315)
Gráfica
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | \/ 15 || ____ |\/ 15 | ____ | |\/ 15 || ____ |\/ 15 |
\/ 15 *|pi*I + log|-tan(1/2) + ------|| \/ 15 *log|------| \/ 15 *|pi*I + log|------|| \/ 15 *log|------ + tan(1/2)|
\ \ 3 // \ 3 / \ \ 3 // \ 3 /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
15 15 15 15
−1515log(315)+1515log(tan(21)+315)−1515(log(−tan(21)+315)+iπ)+1515(log(315)+iπ)
=
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | \/ 15 || ____ |\/ 15 | ____ | |\/ 15 || ____ |\/ 15 |
\/ 15 *|pi*I + log|-tan(1/2) + ------|| \/ 15 *log|------| \/ 15 *|pi*I + log|------|| \/ 15 *log|------ + tan(1/2)|
\ \ 3 // \ 3 / \ \ 3 // \ 3 /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
15 15 15 15
−1515log(315)+1515log(tan(21)+315)−1515(log(−tan(21)+315)+iπ)+1515(log(315)+iπ)
-sqrt(15)*(pi*i + log(-tan(1/2) + sqrt(15)/3))/15 - sqrt(15)*log(sqrt(15)/3)/15 + sqrt(15)*(pi*i + log(sqrt(15)/3))/15 + sqrt(15)*log(sqrt(15)/3 + tan(1/2))/15
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.