Sr Examen
Integral de cos(sqrt(2)*y)*y^2*e^(y*2) dy
Solución
Ha introducido
[src]
t / | | / ___ \ 2 y*2 | cos\\/ 2 *y/*y *E dy | / 0
$$\int\limits_{0}^{t} e^{2 y} y^{2} \cos{\left(\sqrt{2} y \right)}\, dy$$
Integral((cos(sqrt(2)*y)*y^2)*E^(y*2), (y, 0, t))
Respuesta (Indefinida)
[src]
/ / | | | / ___ \ 2 y*2 | 2 / ___ \ y*2 | cos\\/ 2 *y/*y *E dy = C + | y *cos\\/ 2 *y/*e dy | | / /
$$\int e^{2 y} y^{2} \cos{\left(\sqrt{2} y \right)}\, dy = C + \int y^{2} e^{2 y} \cos{\left(\sqrt{2} y \right)}\, dy$$
Respuesta
[src]
/ ___\ 2*t / ___\ 2*t 2 / ___\ 2*t ___ 2*t / ___\ ___ 2*t / ___\ ___ 2 2*t / ___\ 1 cos\t*\/ 2 /*e t*cos\t*\/ 2 /*e t *cos\t*\/ 2 /*e 5*\/ 2 *e *sin\t*\/ 2 / 2*t*\/ 2 *e *sin\t*\/ 2 / \/ 2 *t *e *sin\t*\/ 2 / -- - ----------------- - ------------------- + -------------------- + ------------------------- - --------------------------- + -------------------------- 27 27 9 3 54 9 6
$$\frac{\sqrt{2} t^{2} e^{2 t} \sin{\left(\sqrt{2} t \right)}}{6} + \frac{t^{2} e^{2 t} \cos{\left(\sqrt{2} t \right)}}{3} - \frac{2 \sqrt{2} t e^{2 t} \sin{\left(\sqrt{2} t \right)}}{9} - \frac{t e^{2 t} \cos{\left(\sqrt{2} t \right)}}{9} + \frac{5 \sqrt{2} e^{2 t} \sin{\left(\sqrt{2} t \right)}}{54} - \frac{e^{2 t} \cos{\left(\sqrt{2} t \right)}}{27} + \frac{1}{27}$$
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/ ___\ 2*t / ___\ 2*t 2 / ___\ 2*t ___ 2*t / ___\ ___ 2*t / ___\ ___ 2 2*t / ___\ 1 cos\t*\/ 2 /*e t*cos\t*\/ 2 /*e t *cos\t*\/ 2 /*e 5*\/ 2 *e *sin\t*\/ 2 / 2*t*\/ 2 *e *sin\t*\/ 2 / \/ 2 *t *e *sin\t*\/ 2 / -- - ----------------- - ------------------- + -------------------- + ------------------------- - --------------------------- + -------------------------- 27 27 9 3 54 9 6
$$\frac{\sqrt{2} t^{2} e^{2 t} \sin{\left(\sqrt{2} t \right)}}{6} + \frac{t^{2} e^{2 t} \cos{\left(\sqrt{2} t \right)}}{3} - \frac{2 \sqrt{2} t e^{2 t} \sin{\left(\sqrt{2} t \right)}}{9} - \frac{t e^{2 t} \cos{\left(\sqrt{2} t \right)}}{9} + \frac{5 \sqrt{2} e^{2 t} \sin{\left(\sqrt{2} t \right)}}{54} - \frac{e^{2 t} \cos{\left(\sqrt{2} t \right)}}{27} + \frac{1}{27}$$
1/27 - cos(t*sqrt(2))*exp(2*t)/27 - t*cos(t*sqrt(2))*exp(2*t)/9 + t^2*cos(t*sqrt(2))*exp(2*t)/3 + 5*sqrt(2)*exp(2*t)*sin(t*sqrt(2))/54 - 2*t*sqrt(2)*exp(2*t)*sin(t*sqrt(2))/9 + sqrt(2)*t^2*exp(2*t)*sin(t*sqrt(2))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.