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