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