Sr Examen
Integral de (x+5)^4sin(x+5)^5 dx
Solución
Ha introducido
[src]
1 / | | 4 5 | (x + 5) *sin (x + 5) dx | / 0
$$\int\limits_{0}^{1} \left(x + 5\right)^{4} \sin^{5}{\left(x + 5 \right)}\, dx$$
Integral((x + 5)^4*sin(x + 5)^5, (x, 0, 1))
Gráfica
Respuesta
[src]
5 5 5 5 3 2 4 2 3 4 4 2 3 4 3 2
111616384*cos (6) 862772*sin (5) 2708944*sin (6) 41544184*cos (5) 61267232*cos (6)*sin (6) 17297128*sin (6)*cos(6) 289456*cos (5)*sin (5) 43424*cos (5)*sin(5) 139648*cos (6)*sin(6) 922112*cos (6)*sin (6) 7449103*sin (5)*cos(5) 24449132*cos (5)*sin (5)
- ----------------- - -------------- + --------------- + ---------------- - ------------------------ - ----------------------- - ---------------------- - -------------------- + --------------------- + ---------------------- + ---------------------- + ------------------------
253125 3375 5625 253125 50625 16875 675 225 375 1125 16875 50625
$$- \frac{111616384 \cos^{5}{\left(6 \right)}}{253125} + \frac{139648 \sin{\left(6 \right)} \cos^{4}{\left(6 \right)}}{375} - \frac{61267232 \sin^{2}{\left(6 \right)} \cos^{3}{\left(6 \right)}}{50625} + \frac{922112 \sin^{3}{\left(6 \right)} \cos^{2}{\left(6 \right)}}{1125} - \frac{17297128 \sin^{4}{\left(6 \right)} \cos{\left(6 \right)}}{16875} + \frac{2708944 \sin^{5}{\left(6 \right)}}{5625} + \frac{41544184 \cos^{5}{\left(5 \right)}}{253125} - \frac{43424 \sin{\left(5 \right)} \cos^{4}{\left(5 \right)}}{225} + \frac{24449132 \sin^{2}{\left(5 \right)} \cos^{3}{\left(5 \right)}}{50625} - \frac{289456 \sin^{3}{\left(5 \right)} \cos^{2}{\left(5 \right)}}{675} + \frac{7449103 \sin^{4}{\left(5 \right)} \cos{\left(5 \right)}}{16875} - \frac{862772 \sin^{5}{\left(5 \right)}}{3375}$$
=
=
5 5 5 5 3 2 4 2 3 4 4 2 3 4 3 2
111616384*cos (6) 862772*sin (5) 2708944*sin (6) 41544184*cos (5) 61267232*cos (6)*sin (6) 17297128*sin (6)*cos(6) 289456*cos (5)*sin (5) 43424*cos (5)*sin(5) 139648*cos (6)*sin(6) 922112*cos (6)*sin (6) 7449103*sin (5)*cos(5) 24449132*cos (5)*sin (5)
- ----------------- - -------------- + --------------- + ---------------- - ------------------------ - ----------------------- - ---------------------- - -------------------- + --------------------- + ---------------------- + ---------------------- + ------------------------
253125 3375 5625 253125 50625 16875 675 225 375 1125 16875 50625
$$- \frac{111616384 \cos^{5}{\left(6 \right)}}{253125} + \frac{139648 \sin{\left(6 \right)} \cos^{4}{\left(6 \right)}}{375} - \frac{61267232 \sin^{2}{\left(6 \right)} \cos^{3}{\left(6 \right)}}{50625} + \frac{922112 \sin^{3}{\left(6 \right)} \cos^{2}{\left(6 \right)}}{1125} - \frac{17297128 \sin^{4}{\left(6 \right)} \cos{\left(6 \right)}}{16875} + \frac{2708944 \sin^{5}{\left(6 \right)}}{5625} + \frac{41544184 \cos^{5}{\left(5 \right)}}{253125} - \frac{43424 \sin{\left(5 \right)} \cos^{4}{\left(5 \right)}}{225} + \frac{24449132 \sin^{2}{\left(5 \right)} \cos^{3}{\left(5 \right)}}{50625} - \frac{289456 \sin^{3}{\left(5 \right)} \cos^{2}{\left(5 \right)}}{675} + \frac{7449103 \sin^{4}{\left(5 \right)} \cos{\left(5 \right)}}{16875} - \frac{862772 \sin^{5}{\left(5 \right)}}{3375}$$
-111616384*cos(6)^5/253125 - 862772*sin(5)^5/3375 + 2708944*sin(6)^5/5625 + 41544184*cos(5)^5/253125 - 61267232*cos(6)^3*sin(6)^2/50625 - 17297128*sin(6)^4*cos(6)/16875 - 289456*cos(5)^2*sin(5)^3/675 - 43424*cos(5)^4*sin(5)/225 + 139648*cos(6)^4*sin(6)/375 + 922112*cos(6)^2*sin(6)^3/1125 + 7449103*sin(5)^4*cos(5)/16875 + 24449132*cos(5)^3*sin(5)^2/50625
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.