Sr Examen
Integral de (e^(4x)-1)^(1/2)/sin2x dx
Solución
Ha introducido
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1 / | | __________ | / 4*x | \/ E - 1 | ------------- dx | sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{e^{4 x} - 1}}{\sin{\left(2 x \right)}}\, dx$$
Integral(sqrt(E^(4*x) - 1)/sin(2*x), (x, 0, 1))
Respuesta (Indefinida)
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/ / | | | __________ | _______________________________ | / 4*x | / / x\ / 2*x\ / x\ | \/ E - 1 | \/ \1 + e /*\1 + e /*\-1 + e / | ------------- dx = C + | ---------------------------------- dx | sin(2*x) | sin(2*x) | | / /
$$\int \frac{\sqrt{e^{4 x} - 1}}{\sin{\left(2 x \right)}}\, dx = C + \int \frac{\sqrt{\left(e^{x} - 1\right) \left(e^{x} + 1\right) \left(e^{2 x} + 1\right)}}{\sin{\left(2 x \right)}}\, dx$$
Respuesta
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1 / | | ________ __________ _________ | / x / 2*x / x | \/ 1 + e *\/ 1 + e *\/ -1 + e | -------------------------------------- dx | sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{e^{x} - 1} \sqrt{e^{x} + 1} \sqrt{e^{2 x} + 1}}{\sin{\left(2 x \right)}}\, dx$$
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1 / | | ________ __________ _________ | / x / 2*x / x | \/ 1 + e *\/ 1 + e *\/ -1 + e | -------------------------------------- dx | sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{e^{x} - 1} \sqrt{e^{x} + 1} \sqrt{e^{2 x} + 1}}{\sin{\left(2 x \right)}}\, dx$$
Integral(sqrt(1 + exp(x))*sqrt(1 + exp(2*x))*sqrt(-1 + exp(x))/sin(2*x), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.