Sr Examen
Integral de x*sin(2x)/(x^2+9)^2 dx
Solución
Ha introducido
[src]
oo / | | x*sin(2*x) | ---------- dx | 2 | / 2 \ | \x + 9/ | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{x \sin{\left(2 x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx$$
Integral((x*sin(2*x))/(x^2 + 9)^2, (x, -oo, oo))
Respuesta (Indefinida)
[src]
/ / | | | x*sin(2*x) | x*cos(x)*sin(x) | ---------- dx = C + 2* | --------------- dx | 2 | 2 | / 2 \ | / 2\ | \x + 9/ | \9 + x / | | / /
$$\int \frac{x \sin{\left(2 x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx = C + 2 \int \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx$$
Respuesta
[src]
____ / ____ ____ \
\/ pi *\- 27*\/ pi *sinh(6) + 27*\/ pi *cosh(6)/
------------------------------------------------
81
$$\frac{\sqrt{\pi} \left(- 27 \sqrt{\pi} \sinh{\left(6 \right)} + 27 \sqrt{\pi} \cosh{\left(6 \right)}\right)}{81}$$
=
=
____ / ____ ____ \
\/ pi *\- 27*\/ pi *sinh(6) + 27*\/ pi *cosh(6)/
------------------------------------------------
81
$$\frac{\sqrt{\pi} \left(- 27 \sqrt{\pi} \sinh{\left(6 \right)} + 27 \sqrt{\pi} \cosh{\left(6 \right)}\right)}{81}$$
sqrt(pi)*(-27*sqrt(pi)*sinh(6) + 27*sqrt(pi)*cosh(6))/81
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.