Integral de 1/(6+8sin(x)+5cos(x)) dx
Solución
Respuesta (Indefinida)
[src]
/ ____ / ____ /x\\ ____ / ____ /x\\
| \/ 53 *log|8 + \/ 53 + tan|-|| \/ 53 *log|8 - \/ 53 + tan|-||
| 1 \ \2// \ \2//
| ----------------------- dx = C - ------------------------------- + -------------------------------
| 6 + 8*sin(x) + 5*cos(x) 53 53
|
/
∫(8sin(x)+6)+5cos(x)1dx=C+5353log(tan(2x)−53+8)−5353log(tan(2x)+53+8)
Gráfica
____ / ____\ ____ / ____ \ ____ / ____\ ____ / ____ \
\/ 53 *log\8 - \/ 53 / \/ 53 *log\8 + \/ 53 + tan(1/2)/ \/ 53 *log\8 + \/ 53 / \/ 53 *log\8 - \/ 53 + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
53 53 53 53
−5353log(tan(21)+53+8)+5353log(−53+tan(21)+8)−5353log(8−53)+5353log(53+8)
=
____ / ____\ ____ / ____ \ ____ / ____\ ____ / ____ \
\/ 53 *log\8 - \/ 53 / \/ 53 *log\8 + \/ 53 + tan(1/2)/ \/ 53 *log\8 + \/ 53 / \/ 53 *log\8 - \/ 53 + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
53 53 53 53
−5353log(tan(21)+53+8)+5353log(−53+tan(21)+8)−5353log(8−53)+5353log(53+8)
-sqrt(53)*log(8 - sqrt(53))/53 - sqrt(53)*log(8 + sqrt(53) + tan(1/2))/53 + sqrt(53)*log(8 + sqrt(53))/53 + sqrt(53)*log(8 - sqrt(53) + tan(1/2))/53
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.