Integral de (cos^5)4x dx
Solución
Respuesta (Indefinida)
[src]
/
| 5 5 4 3 2 2 3
| 5 596*cos (x) 32*x*sin (x) 32*sin (x)*cos(x) 208*cos (x)*sin (x) 4 16*x*cos (x)*sin (x)
| cos (x)*4*x dx = C + ----------- + ------------ + ----------------- + ------------------- + 4*x*cos (x)*sin(x) + --------------------
| 225 15 15 45 3
/
∫x4cos5(x)dx=C+1532xsin5(x)+316xsin3(x)cos2(x)+4xsin(x)cos4(x)+1532sin4(x)cos(x)+45208sin2(x)cos3(x)+225596cos5(x)
Gráfica
5/2 5/2 2 ___________ 3/2 ___________ 2 3/2
/ ___\ / ___\ / ___\ / ___ / ___\ / ___\ / ___ / ___\ / ___\ / ___\
|1 \/ 2 | |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | |1 \/ 2 |
596*|- + -----| 4*pi*|- - -----| 32*|- - -----| * / - + ----- 208*|- + -----| *|- - -----| pi* / - - ----- *|- + -----| 2*pi*|- - -----| *|- + -----|
596 \2 4 / \2 4 / \2 4 / \/ 2 4 \2 4 / \2 4 / \/ 2 4 \2 4 / \2 4 / \2 4 /
- --- + ------------------ + ------------------- + -------------------------------- + ------------------------------ + -------------------------------- + -------------------------------
225 225 15 15 45 2 3
−225596+154π(21−42)25+1532(21−42)242+21+32π(21−42)23(42+21)+2π21−42(42+21)2+45208(21−42)(42+21)23+225596(42+21)25
=
5/2 5/2 2 ___________ 3/2 ___________ 2 3/2
/ ___\ / ___\ / ___\ / ___ / ___\ / ___\ / ___ / ___\ / ___\ / ___\
|1 \/ 2 | |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | |1 \/ 2 |
596*|- + -----| 4*pi*|- - -----| 32*|- - -----| * / - + ----- 208*|- + -----| *|- - -----| pi* / - - ----- *|- + -----| 2*pi*|- - -----| *|- + -----|
596 \2 4 / \2 4 / \2 4 / \/ 2 4 \2 4 / \2 4 / \/ 2 4 \2 4 / \2 4 / \2 4 /
- --- + ------------------ + ------------------- + -------------------------------- + ------------------------------ + -------------------------------- + -------------------------------
225 225 15 15 45 2 3
−225596+154π(21−42)25+1532(21−42)242+21+32π(21−42)23(42+21)+2π21−42(42+21)2+45208(21−42)(42+21)23+225596(42+21)25
-596/225 + 596*(1/2 + sqrt(2)/4)^(5/2)/225 + 4*pi*(1/2 - sqrt(2)/4)^(5/2)/15 + 32*(1/2 - sqrt(2)/4)^2*sqrt(1/2 + sqrt(2)/4)/15 + 208*(1/2 + sqrt(2)/4)^(3/2)*(1/2 - sqrt(2)/4)/45 + pi*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^2/2 + 2*pi*(1/2 - sqrt(2)/4)^(3/2)*(1/2 + sqrt(2)/4)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.