Sr Examen
Integral de x*e^x*sin(x)^2 dx
Solución
Ha introducido
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1 / | | x 2 | x*E *sin (x) dx | / 0
$$\int\limits_{0}^{1} e^{x} x \sin^{2}{\left(x \right)}\, dx$$
Integral((x*E^x)*sin(x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 x 2 x 2 x 2 x x x | x 2 14*cos (x)*e 11*sin (x)*e 2*x*cos (x)*e 3*x*sin (x)*e 4*cos(x)*e *sin(x) 2*x*cos(x)*e *sin(x) | x*E *sin (x) dx = C - ------------- - ------------- + -------------- + -------------- + ------------------ - -------------------- | 25 25 5 5 25 5 /
$$\int e^{x} x \sin^{2}{\left(x \right)}\, dx = C + \frac{3 x e^{x} \sin^{2}{\left(x \right)}}{5} - \frac{2 x e^{x} \sin{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{2 x e^{x} \cos^{2}{\left(x \right)}}{5} - \frac{11 e^{x} \sin^{2}{\left(x \right)}}{25} + \frac{4 e^{x} \sin{\left(x \right)} \cos{\left(x \right)}}{25} - \frac{14 e^{x} \cos^{2}{\left(x \right)}}{25}$$
Gráfica
Respuesta
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2 2 14 4*E*cos (1) 4*E*sin (1) 6*E*cos(1)*sin(1) -- - ----------- + ----------- - ----------------- 25 25 25 25
$$- \frac{6 e \sin{\left(1 \right)} \cos{\left(1 \right)}}{25} - \frac{4 e \cos^{2}{\left(1 \right)}}{25} + \frac{4 e \sin^{2}{\left(1 \right)}}{25} + \frac{14}{25}$$
=
=
2 2 14 4*E*cos (1) 4*E*sin (1) 6*E*cos(1)*sin(1) -- - ----------- + ----------- - ----------------- 25 25 25 25
$$- \frac{6 e \sin{\left(1 \right)} \cos{\left(1 \right)}}{25} - \frac{4 e \cos^{2}{\left(1 \right)}}{25} + \frac{4 e \sin^{2}{\left(1 \right)}}{25} + \frac{14}{25}$$
14/25 - 4*E*cos(1)^2/25 + 4*E*sin(1)^2/25 - 6*E*cos(1)*sin(1)/25
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.