Sr Examen
Integral de (sin^3(mx))/(x*sqrt(x)) dx
Solución
Ha introducido
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oo / | | 3 | sin (m*x) | --------- dx | ___ | x*\/ x | / 0
$$\int\limits_{0}^{\infty} \frac{\sin^{3}{\left(m x \right)}}{\sqrt{x} x}\, dx$$
Integral(sin(m*x)^3/((x*sqrt(x))), (x, 0, oo))
Respuesta
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/ ___ ____ 5/2 ___ ____ 5/2 | \/ 6 *\/ pi *polar_lift (m) 3*\/ 2 *\/ pi *polar_lift (m) |- ----------------------------- + ------------------------------- for 2*|arg(m)| = 0 | 2 2 | 4*m 4*m | | oo | / < | | | 3 | | sin (m*x) | | --------- dx otherwise | | 3/2 | | x | | | / \ 0
$$\begin{cases} - \frac{\sqrt{6} \sqrt{\pi} \operatorname{polar\_lift}^{\frac{5}{2}}{\left(m \right)}}{4 m^{2}} + \frac{3 \sqrt{2} \sqrt{\pi} \operatorname{polar\_lift}^{\frac{5}{2}}{\left(m \right)}}{4 m^{2}} & \text{for}\: 2 \left|{\arg{\left(m \right)}}\right| = 0 \\\int\limits_{0}^{\infty} \frac{\sin^{3}{\left(m x \right)}}{x^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}$$
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/ ___ ____ 5/2 ___ ____ 5/2 | \/ 6 *\/ pi *polar_lift (m) 3*\/ 2 *\/ pi *polar_lift (m) |- ----------------------------- + ------------------------------- for 2*|arg(m)| = 0 | 2 2 | 4*m 4*m | | oo | / < | | | 3 | | sin (m*x) | | --------- dx otherwise | | 3/2 | | x | | | / \ 0
$$\begin{cases} - \frac{\sqrt{6} \sqrt{\pi} \operatorname{polar\_lift}^{\frac{5}{2}}{\left(m \right)}}{4 m^{2}} + \frac{3 \sqrt{2} \sqrt{\pi} \operatorname{polar\_lift}^{\frac{5}{2}}{\left(m \right)}}{4 m^{2}} & \text{for}\: 2 \left|{\arg{\left(m \right)}}\right| = 0 \\\int\limits_{0}^{\infty} \frac{\sin^{3}{\left(m x \right)}}{x^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}$$
Piecewise((-sqrt(6)*sqrt(pi)*polar_lift(m)^(5/2)/(4*m^2) + 3*sqrt(2)*sqrt(pi)*polar_lift(m)^(5/2)/(4*m^2), 2*Abs(arg(m)) = 0), (Integral(sin(m*x)^3/x^(3/2), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.