Sr Examen
Integral de sinh2x/sqrt(1-sinh^2(x)) dx
Solución
Ha introducido
[src]
1/2 / | | sinh(2*x) | ----------------- dx | ______________ | / 2 | \/ 1 - sinh (x) | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{1 - \sinh^{2}{\left(x \right)}}}\, dx$$
Integral(sinh(2*x)/sqrt(1 - sinh(x)^2), (x, -1/2, 1/2))
Respuesta (Indefinida)
[src]
/ / | | | sinh(2*x) | sinh(2*x) | ----------------- dx = C + | --------------------------------- dx | ______________ | _______________________________ | / 2 | \/ -(1 + sinh(x))*(-1 + sinh(x)) | \/ 1 - sinh (x) | | / /
$$\int \frac{\sinh{\left(2 x \right)}}{\sqrt{1 - \sinh^{2}{\left(x \right)}}}\, dx = C + \int \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$
Respuesta
[src]
1/2 / | | sinh(2*x) | --------------------------------- dx | _______________________________ | \/ -(1 + sinh(x))*(-1 + sinh(x)) | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$
=
=
1/2 / | | sinh(2*x) | --------------------------------- dx | _______________________________ | \/ -(1 + sinh(x))*(-1 + sinh(x)) | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$
Integral(sinh(2*x)/sqrt(-(1 + sinh(x))*(-1 + sinh(x))), (x, -1/2, 1/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.