Integral de xsinx÷cos^3x dx
Solución
Respuesta (Indefinida)
[src]
/ /x\ 3/x\ 4/x\ 2/x\
| 2*tan|-| 2*tan |-| x*tan |-| 2*x*tan |-|
| x*sin(x) x \2/ \2/ \2/ \2/
| -------- dx = C + ------------------------- - ------------------------- + ------------------------- + ------------------------- + -------------------------
| 3 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ 4/x\
| cos (x) 2 - 4*tan |-| + 2*tan |-| 2 - 4*tan |-| + 2*tan |-| 2 - 4*tan |-| + 2*tan |-| 2 - 4*tan |-| + 2*tan |-| 2 - 4*tan |-| + 2*tan |-|
| \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/
/
∫cos3(x)xsin(x)dx=C+2tan4(2x)−4tan2(2x)+2xtan4(2x)+2tan4(2x)−4tan2(2x)+22xtan2(2x)+2tan4(2x)−4tan2(2x)+2x+2tan4(2x)−4tan2(2x)+22tan3(2x)−2tan4(2x)−4tan2(2x)+22tan(2x)
Gráfica
4 2 3
1 tan (1/2) 2*tan(1/2) 2*tan (1/2) 2*tan (1/2)
----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
2 4 2 4 2 4 2 4 2 4
2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2)
−−4tan2(21)+2tan4(21)+22tan(21)+−4tan2(21)+2tan4(21)+2tan4(21)+−4tan2(21)+2tan4(21)+22tan3(21)+−4tan2(21)+2tan4(21)+22tan2(21)+−4tan2(21)+2tan4(21)+21
=
4 2 3
1 tan (1/2) 2*tan(1/2) 2*tan (1/2) 2*tan (1/2)
----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
2 4 2 4 2 4 2 4 2 4
2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2) 2 - 4*tan (1/2) + 2*tan (1/2)
−−4tan2(21)+2tan4(21)+22tan(21)+−4tan2(21)+2tan4(21)+2tan4(21)+−4tan2(21)+2tan4(21)+22tan3(21)+−4tan2(21)+2tan4(21)+22tan2(21)+−4tan2(21)+2tan4(21)+21
1/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + tan(1/2)^4/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) - 2*tan(1/2)/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + 2*tan(1/2)^2/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + 2*tan(1/2)^3/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.