Sr Examen
Integral de 2*sin(3*x)^2*cos(3*x)^6 dx
Solución
Ha introducido
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1 / | | 2 6 | 2*sin (3*x)*cos (3*x) dx | / 0
$$\int\limits_{0}^{1} 2 \sin^{2}{\left(3 x \right)} \cos^{6}{\left(3 x \right)}\, dx$$
Integral((2*sin(3*x)^2)*cos(3*x)^6, (x, 0, 1))
Respuesta (Indefinida)
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/ | 7 8 8 7 3 5 5 3 2 6 6 2 4 4 | 2 6 5*cos (3*x)*sin(3*x) 5*x*cos (3*x) 5*x*sin (3*x) 5*sin (3*x)*cos(3*x) 55*cos (3*x)*sin (3*x) 73*cos (3*x)*sin (3*x) 5*x*cos (3*x)*sin (3*x) 5*x*cos (3*x)*sin (3*x) 15*x*cos (3*x)*sin (3*x) | 2*sin (3*x)*cos (3*x) dx = C - -------------------- + ------------- + ------------- + -------------------- + ---------------------- + ---------------------- + ----------------------- + ----------------------- + ------------------------ | 192 64 64 192 576 576 16 16 32 /
$$\int 2 \sin^{2}{\left(3 x \right)} \cos^{6}{\left(3 x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(3 x \right)}}{64} + \frac{5 x \sin^{6}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{16} + \frac{15 x \sin^{4}{\left(3 x \right)} \cos^{4}{\left(3 x \right)}}{32} + \frac{5 x \sin^{2}{\left(3 x \right)} \cos^{6}{\left(3 x \right)}}{16} + \frac{5 x \cos^{8}{\left(3 x \right)}}{64} + \frac{5 \sin^{7}{\left(3 x \right)} \cos{\left(3 x \right)}}{192} + \frac{55 \sin^{5}{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{576} + \frac{73 \sin^{3}{\left(3 x \right)} \cos^{5}{\left(3 x \right)}}{576} - \frac{5 \sin{\left(3 x \right)} \cos^{7}{\left(3 x \right)}}{192}$$
Gráfica
Respuesta
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7 5 3 5 cos (3)*sin(3) cos (3)*sin(3) 5*cos(3)*sin(3) 5*cos (3)*sin(3) -- - -------------- + -------------- + --------------- + ---------------- 64 12 72 192 288
$$\frac{5 \sin{\left(3 \right)} \cos{\left(3 \right)}}{192} + \frac{5 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{288} + \frac{\sin{\left(3 \right)} \cos^{5}{\left(3 \right)}}{72} - \frac{\sin{\left(3 \right)} \cos^{7}{\left(3 \right)}}{12} + \frac{5}{64}$$
=
=
7 5 3 5 cos (3)*sin(3) cos (3)*sin(3) 5*cos(3)*sin(3) 5*cos (3)*sin(3) -- - -------------- + -------------- + --------------- + ---------------- 64 12 72 192 288
$$\frac{5 \sin{\left(3 \right)} \cos{\left(3 \right)}}{192} + \frac{5 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{288} + \frac{\sin{\left(3 \right)} \cos^{5}{\left(3 \right)}}{72} - \frac{\sin{\left(3 \right)} \cos^{7}{\left(3 \right)}}{12} + \frac{5}{64}$$
5/64 - cos(3)^7*sin(3)/12 + cos(3)^5*sin(3)/72 + 5*cos(3)*sin(3)/192 + 5*cos(3)^3*sin(3)/288
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.