Sr Examen
Integral de x^2*cos(x)/(x^2+1)^2 dx
Solución
Ha introducido
[src]
oo / | | 2 | x *cos(x) | --------- dx | 2 | / 2 \ | \x + 1/ | / 0
$$\int\limits_{0}^{\infty} \frac{x^{2} \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx$$
Integral((x^2*cos(x))/(x^2 + 1)^2, (x, 0, oo))
Respuesta (Indefinida)
[src]
/ / | | | 2 | 2 | x *cos(x) | x *cos(x) | --------- dx = C + | --------- dx | 2 | 2 | / 2 \ | / 2\ | \x + 1/ | \1 + x / | | / /
$$\int \frac{x^{2} \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx = C + \int \frac{x^{2} \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx$$
Respuesta
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____ / ____ /cosh(1) sinh(1)\ ____ /cosh(1) sinh(1)\\
4*\/ pi *|\/ pi *|------- + -------| - 2*\/ pi *|------- + -------||
\ \ 16 16 / \ 32 32 //
$$4 \sqrt{\pi} \left(- 2 \sqrt{\pi} \left(\frac{\sinh{\left(1 \right)}}{32} + \frac{\cosh{\left(1 \right)}}{32}\right) + \sqrt{\pi} \left(\frac{\sinh{\left(1 \right)}}{16} + \frac{\cosh{\left(1 \right)}}{16}\right)\right)$$
=
=
____ / ____ /cosh(1) sinh(1)\ ____ /cosh(1) sinh(1)\\
4*\/ pi *|\/ pi *|------- + -------| - 2*\/ pi *|------- + -------||
\ \ 16 16 / \ 32 32 //
$$4 \sqrt{\pi} \left(- 2 \sqrt{\pi} \left(\frac{\sinh{\left(1 \right)}}{32} + \frac{\cosh{\left(1 \right)}}{32}\right) + \sqrt{\pi} \left(\frac{\sinh{\left(1 \right)}}{16} + \frac{\cosh{\left(1 \right)}}{16}\right)\right)$$
4*sqrt(pi)*(sqrt(pi)*(cosh(1)/16 + sinh(1)/16) - 2*sqrt(pi)*(cosh(1)/32 + sinh(1)/32))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.