Sr Examen
Integral de ((x-1)sin(x))/((x^2+9)^2) dx
Solución
Ha introducido
[src]
oo / | | (x - 1)*sin(x) | -------------- dx | 2 | / 2 \ | \x + 9/ | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{\left(x - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx$$
Integral(((x - 1)*sin(x))/(x^2 + 9)^2, (x, -oo, oo))
Respuesta (Indefinida)
[src]
/ / / | | | | (x - 1)*sin(x) | sin(x) | x*sin(x) | -------------- dx = C - | --------- dx + | --------- dx | 2 | 2 | 2 | / 2 \ | / 2\ | / 2\ | \x + 9/ | \9 + x / | \9 + x / | | | / / /
$$\int \frac{\left(x - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx = C - \int \frac{\sin{\left(x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx + \int \frac{x \sin{\left(x \right)}}{\left(x^{2} + 9\right)^{2}}\, dx$$
Respuesta
[src]
/ ____ ____ \
____ | 27*\/ pi *sinh(3) 27*\/ pi *cosh(3)|
4*\/ pi *|- ----------------- + -----------------|
\ 8 8 /
--------------------------------------------------
81
$$\frac{4 \sqrt{\pi} \left(- \frac{27 \sqrt{\pi} \sinh{\left(3 \right)}}{8} + \frac{27 \sqrt{\pi} \cosh{\left(3 \right)}}{8}\right)}{81}$$
=
=
/ ____ ____ \
____ | 27*\/ pi *sinh(3) 27*\/ pi *cosh(3)|
4*\/ pi *|- ----------------- + -----------------|
\ 8 8 /
--------------------------------------------------
81
$$\frac{4 \sqrt{\pi} \left(- \frac{27 \sqrt{\pi} \sinh{\left(3 \right)}}{8} + \frac{27 \sqrt{\pi} \cosh{\left(3 \right)}}{8}\right)}{81}$$
4*sqrt(pi)*(-27*sqrt(pi)*sinh(3)/8 + 27*sqrt(pi)*cosh(3)/8)/81
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.