Integral de (cos(2x))/(cos(x)+sen(x)) dx
Solución
Respuesta (Indefinida)
[src]
/ ___ / ___ /x\\ /x\ ___ / ___ /x\\ ___ / ___ /x\\ ___ / ___ /x\\ ___ 2/x\ / ___ /x\\ ___ 2/x\ / ___ /x\\
| \/ 2 *log|-1 - \/ 2 + tan|-|| 8*tan|-| \/ 2 *log|-1 + \/ 2 + tan|-|| 2*\/ 2 *log|-1 - \/ 2 + tan|-|| 2*\/ 2 *log|-1 + \/ 2 + tan|-|| 2*\/ 2 *tan |-|*log|-1 - \/ 2 + tan|-|| 2*\/ 2 *tan |-|*log|-1 + \/ 2 + tan|-||
| cos(2*x) 8 \ \2// \2/ \ \2// \ \2// \ \2// \2/ \ \2// \2/ \ \2//
| --------------- dx = C + ------------- + ------------------------------ + ------------- - ------------------------------ - -------------------------------- + -------------------------------- - ---------------------------------------- + ----------------------------------------
| cos(x) + sin(x) 2/x\ 2 2/x\ 2 2/x\ 2/x\ 2/x\ 2/x\
| 4 + 4*tan |-| 4 + 4*tan |-| 4 + 4*tan |-| 4 + 4*tan |-| 4 + 4*tan |-| 4 + 4*tan |-|
/ \2/ \2/ \2/ \2/ \2/ \2/
∫sin(x)+cos(x)cos(2x)dx=C−22log(tan(2x)−1+2)+22log(tan(2x)−2−1)+4tan2(2x)+422log(tan(2x)−1+2)tan2(2x)+4tan2(2x)+422log(tan(2x)−1+2)−4tan2(2x)+422log(tan(2x)−2−1)tan2(2x)−4tan2(2x)+422log(tan(2x)−2−1)+4tan2(2x)+48tan(2x)+4tan2(2x)+48
Gráfica
___ / / ___ \\ ___ / ___ \ ___ / / ___ \\ ___ / ___ \ ___ 2 / / ___ \\ ___ 2 / ___ \
8 \/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// 8*tan(1/2) \/ 2 *log\-1 + \/ 2 + tan(1/2)/ 2*\/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// 2*\/ 2 *log\-1 + \/ 2 + tan(1/2)/ 2*\/ 2 *tan (1/2)*\pi*I + log\1 + \/ 2 - tan(1/2)// 2*\/ 2 *tan (1/2)*log\-1 + \/ 2 + tan(1/2)/
-2 + --------------- + ---------------------------------------- + --------------- - -------------------------------- - ------------------------------------------ + ---------------------------------- - ---------------------------------------------------- + --------------------------------------------
2 2 2 2 2 2 2 2
4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2)
−2+4tan2(21)+422log(−1+tan(21)+2)+4tan2(21)+422log(−1+tan(21)+2)tan2(21)−22log(−1+tan(21)+2)+4tan2(21)+48tan(21)+4tan2(21)+48−4tan2(21)+422(log(−tan(21)+1+2)+iπ)−4tan2(21)+422(log(−tan(21)+1+2)+iπ)tan2(21)+22(log(−tan(21)+1+2)+iπ)
=
___ / / ___ \\ ___ / ___ \ ___ / / ___ \\ ___ / ___ \ ___ 2 / / ___ \\ ___ 2 / ___ \
8 \/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// 8*tan(1/2) \/ 2 *log\-1 + \/ 2 + tan(1/2)/ 2*\/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// 2*\/ 2 *log\-1 + \/ 2 + tan(1/2)/ 2*\/ 2 *tan (1/2)*\pi*I + log\1 + \/ 2 - tan(1/2)// 2*\/ 2 *tan (1/2)*log\-1 + \/ 2 + tan(1/2)/
-2 + --------------- + ---------------------------------------- + --------------- - -------------------------------- - ------------------------------------------ + ---------------------------------- - ---------------------------------------------------- + --------------------------------------------
2 2 2 2 2 2 2 2
4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2) 4 + 4*tan (1/2)
−2+4tan2(21)+422log(−1+tan(21)+2)+4tan2(21)+422log(−1+tan(21)+2)tan2(21)−22log(−1+tan(21)+2)+4tan2(21)+48tan(21)+4tan2(21)+48−4tan2(21)+422(log(−tan(21)+1+2)+iπ)−4tan2(21)+422(log(−tan(21)+1+2)+iπ)tan2(21)+22(log(−tan(21)+1+2)+iπ)
-2 + 8/(4 + 4*tan(1/2)^2) + sqrt(2)*(pi*i + log(1 + sqrt(2) - tan(1/2)))/2 + 8*tan(1/2)/(4 + 4*tan(1/2)^2) - sqrt(2)*log(-1 + sqrt(2) + tan(1/2))/2 - 2*sqrt(2)*(pi*i + log(1 + sqrt(2) - tan(1/2)))/(4 + 4*tan(1/2)^2) + 2*sqrt(2)*log(-1 + sqrt(2) + tan(1/2))/(4 + 4*tan(1/2)^2) - 2*sqrt(2)*tan(1/2)^2*(pi*i + log(1 + sqrt(2) - tan(1/2)))/(4 + 4*tan(1/2)^2) + 2*sqrt(2)*tan(1/2)^2*log(-1 + sqrt(2) + tan(1/2))/(4 + 4*tan(1/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.