Sr Examen
Integral de cos(k*x)/(1+x^2) dx
Solución
Ha introducido
[src]
oo / | | cos(k*x) | -------- dx | 2 | 1 + x | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{\cos{\left(k x \right)}}{x^{2} + 1}\, dx$$
Integral(cos(k*x)/(1 + x^2), (x, -oo, oo))
Respuesta (Indefinida)
[src]
/ / | | | cos(k*x) | cos(k*x) | -------- dx = C + | -------- dx | 2 | 2 | 1 + x | 1 + x | | / /
$$\int \frac{\cos{\left(k x \right)}}{x^{2} + 1}\, dx = C + \int \frac{\cos{\left(k x \right)}}{x^{2} + 1}\, dx$$
Respuesta
[src]
/ ____ / ____ ____ \ |\/ pi *\\/ pi *cosh(k) - \/ pi *sinh(k)/ for 2*|arg(k)| = 0 | | oo | / | | < | cos(k*x) | | -------- dx otherwise | | 2 | | 1 + x | | | / \ -oo
$$\begin{cases} \sqrt{\pi} \left(- \sqrt{\pi} \sinh{\left(k \right)} + \sqrt{\pi} \cosh{\left(k \right)}\right) & \text{for}\: 2 \left|{\arg{\left(k \right)}}\right| = 0 \\\int\limits_{-\infty}^{\infty} \frac{\cos{\left(k x \right)}}{x^{2} + 1}\, dx & \text{otherwise} \end{cases}$$
=
=
/ ____ / ____ ____ \ |\/ pi *\\/ pi *cosh(k) - \/ pi *sinh(k)/ for 2*|arg(k)| = 0 | | oo | / | | < | cos(k*x) | | -------- dx otherwise | | 2 | | 1 + x | | | / \ -oo
$$\begin{cases} \sqrt{\pi} \left(- \sqrt{\pi} \sinh{\left(k \right)} + \sqrt{\pi} \cosh{\left(k \right)}\right) & \text{for}\: 2 \left|{\arg{\left(k \right)}}\right| = 0 \\\int\limits_{-\infty}^{\infty} \frac{\cos{\left(k x \right)}}{x^{2} + 1}\, dx & \text{otherwise} \end{cases}$$
Piecewise((sqrt(pi)*(sqrt(pi)*cosh(k) - sqrt(pi)*sinh(k)), 2*Abs(arg(k)) = 0), (Integral(cos(k*x)/(1 + x^2), (x, -oo, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.