Integral de x^2sinx^3dx dx
Solución
Respuesta (Indefinida)
[src]
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| 3 2 3 3 2 2
| 2 3 40*cos (x) 2*x *cos (x) 14*x*sin (x) 14*sin (x)*cos(x) 2 2 4*x*cos (x)*sin(x)
| x *sin (x) dx = C + ---------- - ------------ + ------------ + ----------------- - x *sin (x)*cos(x) + ------------------
| 27 3 9 9 3
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$$\int x^{2} \sin^{3}{\left(x \right)}\, dx = C - x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{2 x^{2} \cos^{3}{\left(x \right)}}{3} + \frac{14 x \sin^{3}{\left(x \right)}}{9} + \frac{4 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + \frac{14 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} + \frac{40 \cos^{3}{\left(x \right)}}{27}$$
3 3 2 2
40 14*sin (1) 22*cos (1) 4*cos (1)*sin(1) 5*sin (1)*cos(1)
- -- + ---------- + ---------- + ---------------- + ----------------
27 9 27 3 9
$$- \frac{40}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$
=
3 3 2 2
40 14*sin (1) 22*cos (1) 4*cos (1)*sin(1) 5*sin (1)*cos(1)
- -- + ---------- + ---------- + ---------------- + ----------------
27 9 27 3 9
$$- \frac{40}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$
-40/27 + 14*sin(1)^3/9 + 22*cos(1)^3/27 + 4*cos(1)^2*sin(1)/3 + 5*sin(1)^2*cos(1)/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.