Sr Examen
Integral de exp(x)*cos(x)^2*x dx
Solución
Ha introducido
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1 / | | x 2 | e *cos (x)*x dx | / 0
$$\int\limits_{0}^{1} x e^{x} \cos^{2}{\left(x \right)}\, dx$$
Integral((exp(x)*cos(x)^2)*x, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 x 2 x x 2 x 2 x x | x 2 14*sin (x)*e 11*cos (x)*e 4*cos(x)*e *sin(x) 2*x*sin (x)*e 3*x*cos (x)*e 2*x*cos(x)*e *sin(x) | e *cos (x)*x dx = C - ------------- - ------------- - ------------------ + -------------- + -------------- + -------------------- | 25 25 25 5 5 5 /
$$\int x e^{x} \cos^{2}{\left(x \right)}\, dx = C + \frac{2 x e^{x} \sin^{2}{\left(x \right)}}{5} + \frac{2 x e^{x} \sin{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{3 x e^{x} \cos^{2}{\left(x \right)}}{5} - \frac{14 e^{x} \sin^{2}{\left(x \right)}}{25} - \frac{4 e^{x} \sin{\left(x \right)} \cos{\left(x \right)}}{25} - \frac{11 e^{x} \cos^{2}{\left(x \right)}}{25}$$
Gráfica
Respuesta
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2 2 11 4*E*sin (1) 4*E*cos (1) 6*E*cos(1)*sin(1) -- - ----------- + ----------- + ----------------- 25 25 25 25
$$- \frac{4 e \sin^{2}{\left(1 \right)}}{25} + \frac{4 e \cos^{2}{\left(1 \right)}}{25} + \frac{6 e \sin{\left(1 \right)} \cos{\left(1 \right)}}{25} + \frac{11}{25}$$
=
=
2 2 11 4*E*sin (1) 4*E*cos (1) 6*E*cos(1)*sin(1) -- - ----------- + ----------- + ----------------- 25 25 25 25
$$- \frac{4 e \sin^{2}{\left(1 \right)}}{25} + \frac{4 e \cos^{2}{\left(1 \right)}}{25} + \frac{6 e \sin{\left(1 \right)} \cos{\left(1 \right)}}{25} + \frac{11}{25}$$
11/25 - 4*E*sin(1)^2/25 + 4*E*cos(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.