Sr Examen
Integral de e^xsin(3x)cos(3x) dx
Solución
Ha introducido
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1 / | | x | E *sin(3*x)*cos(3*x) dx | / 0
$$\int\limits_{0}^{1} e^{x} \sin{\left(3 x \right)} \cos{\left(3 x \right)}\, dx$$
Integral((E^x*sin(3*x))*cos(3*x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 x 2 x x | x 3*cos (3*x)*e 3*sin (3*x)*e cos(3*x)*e *sin(3*x) | E *sin(3*x)*cos(3*x) dx = C - -------------- + -------------- + -------------------- | 37 37 37 /
$$\int e^{x} \sin{\left(3 x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{3 e^{x} \sin^{2}{\left(3 x \right)}}{37} + \frac{e^{x} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{37} - \frac{3 e^{x} \cos^{2}{\left(3 x \right)}}{37}$$
Gráfica
Respuesta
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2 2 3 3*E*cos (3) 3*E*sin (3) E*cos(3)*sin(3) -- - ----------- + ----------- + --------------- 37 37 37 37
$$- \frac{3 e \cos^{2}{\left(3 \right)}}{37} + \frac{e \sin{\left(3 \right)} \cos{\left(3 \right)}}{37} + \frac{3 e \sin^{2}{\left(3 \right)}}{37} + \frac{3}{37}$$
=
=
2 2 3 3*E*cos (3) 3*E*sin (3) E*cos(3)*sin(3) -- - ----------- + ----------- + --------------- 37 37 37 37
$$- \frac{3 e \cos^{2}{\left(3 \right)}}{37} + \frac{e \sin{\left(3 \right)} \cos{\left(3 \right)}}{37} + \frac{3 e \sin^{2}{\left(3 \right)}}{37} + \frac{3}{37}$$
3/37 - 3*E*cos(3)^2/37 + 3*E*sin(3)^2/37 + E*cos(3)*sin(3)/37
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.