Sr Examen
Integral de exp^(-3x)*cos^3(2x) dx
Solución
Ha introducido
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1 / | | -3*x 3 | E *cos (2*x) dx | / 0
$$\int\limits_{0}^{1} e^{- 3 x} \cos^{3}{\left(2 x \right)}\, dx$$
Integral(E^(-3*x)*cos(2*x)^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 3 -3*x 3 -3*x 2 -3*x 2 -3*x | -3*x 3 37*cos (2*x)*e 16*sin (2*x)*e 8*sin (2*x)*cos(2*x)*e 14*cos (2*x)*e *sin(2*x) | E *cos (2*x) dx = C - ------------------ + ------------------ - -------------------------- + --------------------------- | 195 195 65 65 /
$$\int e^{- 3 x} \cos^{3}{\left(2 x \right)}\, dx = C + \frac{16 e^{- 3 x} \sin^{3}{\left(2 x \right)}}{195} - \frac{8 e^{- 3 x} \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}}{65} + \frac{14 e^{- 3 x} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{65} - \frac{37 e^{- 3 x} \cos^{3}{\left(2 x \right)}}{195}$$
Gráfica
Respuesta
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3 -3 3 -3 2 -3 2 -3 37 37*cos (2)*e 16*sin (2)*e 8*sin (2)*cos(2)*e 14*cos (2)*e *sin(2) --- - -------------- + -------------- - -------------------- + --------------------- 195 195 195 65 65
$$- \frac{37 \cos^{3}{\left(2 \right)}}{195 e^{3}} + \frac{14 \sin{\left(2 \right)} \cos^{2}{\left(2 \right)}}{65 e^{3}} - \frac{8 \sin^{2}{\left(2 \right)} \cos{\left(2 \right)}}{65 e^{3}} + \frac{16 \sin^{3}{\left(2 \right)}}{195 e^{3}} + \frac{37}{195}$$
=
=
3 -3 3 -3 2 -3 2 -3 37 37*cos (2)*e 16*sin (2)*e 8*sin (2)*cos(2)*e 14*cos (2)*e *sin(2) --- - -------------- + -------------- - -------------------- + --------------------- 195 195 195 65 65
$$- \frac{37 \cos^{3}{\left(2 \right)}}{195 e^{3}} + \frac{14 \sin{\left(2 \right)} \cos^{2}{\left(2 \right)}}{65 e^{3}} - \frac{8 \sin^{2}{\left(2 \right)} \cos{\left(2 \right)}}{65 e^{3}} + \frac{16 \sin^{3}{\left(2 \right)}}{195 e^{3}} + \frac{37}{195}$$
37/195 - 37*cos(2)^3*exp(-3)/195 + 16*sin(2)^3*exp(-3)/195 - 8*sin(2)^2*cos(2)*exp(-3)/65 + 14*cos(2)^2*exp(-3)*sin(2)/65
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.