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