Sr Examen
Integral de (144)(cos^6)*3x dx
Solución
Ha introducido
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1 / | | 6 | 144*cos (x)*3*x dx | / 0
$$\int\limits_{0}^{1} x 3 \cdot 144 \cos^{6}{\left(x \right)}\, dx$$
Integral(((144*cos(x)^6)*3)*x, (x, 0, 1))
Respuesta (Indefinida)
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/ | 6 6 2 6 2 6 2 2 4 2 4 2 | 6 105*sin (x) 99*cos (x) 2 4 135*x *cos (x) 135*x *sin (x) 5 5 3 3 405*x *cos (x)*sin (x) 405*x *cos (x)*sin (x) | 144*cos (x)*3*x dx = C - ----------- + ---------- - 90*cos (x)*sin (x) + -------------- + -------------- + 135*x*sin (x)*cos(x) + 297*x*cos (x)*sin(x) + 360*x*cos (x)*sin (x) + ---------------------- + ---------------------- | 2 2 2 2 2 2 /
$$\int x 3 \cdot 144 \cos^{6}{\left(x \right)}\, dx = C + \frac{135 x^{2} \sin^{6}{\left(x \right)}}{2} + \frac{405 x^{2} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{405 x^{2} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{2} + \frac{135 x^{2} \cos^{6}{\left(x \right)}}{2} + 135 x \sin^{5}{\left(x \right)} \cos{\left(x \right)} + 360 x \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + 297 x \sin{\left(x \right)} \cos^{5}{\left(x \right)} - \frac{105 \sin^{6}{\left(x \right)}}{2} - 90 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{99 \cos^{6}{\left(x \right)}}{2}$$
Gráfica
Respuesta
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2 4 4 2 99 6 6 5 5 3 3 225*cos (1)*sin (1) 405*cos (1)*sin (1) - -- + 15*sin (1) + 117*cos (1) + 135*sin (1)*cos(1) + 297*cos (1)*sin(1) + 360*cos (1)*sin (1) + ------------------- + ------------------- 2 2 2
$$- \frac{99}{2} + 117 \cos^{6}{\left(1 \right)} + 15 \sin^{6}{\left(1 \right)} + 297 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} + \frac{405 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{2} + \frac{225 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{2} + 135 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} + 360 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}$$
=
=
2 4 4 2 99 6 6 5 5 3 3 225*cos (1)*sin (1) 405*cos (1)*sin (1) - -- + 15*sin (1) + 117*cos (1) + 135*sin (1)*cos(1) + 297*cos (1)*sin(1) + 360*cos (1)*sin (1) + ------------------- + ------------------- 2 2 2
$$- \frac{99}{2} + 117 \cos^{6}{\left(1 \right)} + 15 \sin^{6}{\left(1 \right)} + 297 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} + \frac{405 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{2} + \frac{225 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{2} + 135 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} + 360 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}$$
-99/2 + 15*sin(1)^6 + 117*cos(1)^6 + 135*sin(1)^5*cos(1) + 297*cos(1)^5*sin(1) + 360*cos(1)^3*sin(1)^3 + 225*cos(1)^2*sin(1)^4/2 + 405*cos(1)^4*sin(1)^2/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.