Sr Examen
Integral de cos(x)cos(2x)cos(3x)cos(4x)cos(5x) dx
Solución
Ha introducido
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2*pi / | | cos(x)*cos(2*x)*cos(3*x)*cos(4*x)*cos(5*x) dx | / 0
$$\int\limits_{0}^{2 \pi} \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)} \cos{\left(4 x \right)} \cos{\left(5 x \right)}\, dx$$
Integral((((cos(x)*cos(2*x))*cos(3*x))*cos(4*x))*cos(5*x), (x, 0, 2*pi))
Respuesta (Indefinida)
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/ 11 7 15 5 9 13 | 3 4992*sin (x) 1352*sin (x) 1024*sin (x) 274*sin (x) 3536*sin (x) 3584*sin (x) | cos(x)*cos(2*x)*cos(3*x)*cos(4*x)*cos(5*x) dx = C - 9*sin (x) - ------------- - ------------ - ------------- + ----------- + ------------ + ------------- + sin(x) | 11 7 15 5 9 13 /
$$\int \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)} \cos{\left(4 x \right)} \cos{\left(5 x \right)}\, dx = C - \frac{1024 \sin^{15}{\left(x \right)}}{15} + \frac{3584 \sin^{13}{\left(x \right)}}{13} - \frac{4992 \sin^{11}{\left(x \right)}}{11} + \frac{3536 \sin^{9}{\left(x \right)}}{9} - \frac{1352 \sin^{7}{\left(x \right)}}{7} + \frac{274 \sin^{5}{\left(x \right)}}{5} - 9 \sin^{3}{\left(x \right)} + \sin{\left(x \right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.