Sr Examen
Integral de 3x^2cosx^3 dx
Solución
Ha introducido
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1 / | | 2 3 | 3*x *cos (x) dx | / 0
$$\int\limits_{0}^{1} 3 x^{2} \cos^{3}{\left(x \right)}\, dx$$
Integral((3*x^2)*cos(x)^3, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 2 3 | 2 3 40*sin (x) 2 3 14*cos (x)*sin(x) 14*x*cos (x) 2 2 2 | 3*x *cos (x) dx = C - ---------- + 2*x *sin (x) - ----------------- + ------------ + 3*x *cos (x)*sin(x) + 4*x*sin (x)*cos(x) | 9 3 3 /
$$\int 3 x^{2} \cos^{3}{\left(x \right)}\, dx = C + 2 x^{2} \sin^{3}{\left(x \right)} + 3 x^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 4 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{14 x \cos^{3}{\left(x \right)}}{3} - \frac{40 \sin^{3}{\left(x \right)}}{9} - \frac{14 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3}$$
Gráfica
Respuesta
[src]
3 3 2
22*sin (1) 14*cos (1) 2 5*cos (1)*sin(1)
- ---------- + ---------- + 4*sin (1)*cos(1) - ----------------
9 3 3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{9} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \cos^{3}{\left(1 \right)}}{3} + 4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}$$
=
=
3 3 2
22*sin (1) 14*cos (1) 2 5*cos (1)*sin(1)
- ---------- + ---------- + 4*sin (1)*cos(1) - ----------------
9 3 3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{9} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \cos^{3}{\left(1 \right)}}{3} + 4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}$$
-22*sin(1)^3/9 + 14*cos(1)^3/3 + 4*sin(1)^2*cos(1) - 5*cos(1)^2*sin(1)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.