Sr Examen
Integral de cosxd(x)/(1-cosx)^3 dx
Solución
Ha introducido
[src]
pi
--
2
/
|
| cos(x)*d*x
| ------------- dx
| 3
| (1 - cos(x))
|
/
2*atan(1/2)
$$\int\limits_{2 \operatorname{atan}{\left(\frac{1}{2} \right)}}^{\frac{\pi}{2}} \frac{x d \cos{\left(x \right)}}{\left(1 - \cos{\left(x \right)}\right)^{3}}\, dx$$
Integral(((cos(x)*d)*x)/(1 - cos(x))^3, (x, 2*atan(1/2), pi/2))
Respuesta
[src]
/1 log(2) pi\ / 1 11*atan(1/2) log(5/4) 2*log(2)\ d*|-- + ------ + --| - d*|- - - ------------ + -------- + --------| \40 5 10/ \ 5 5 5 5 /
$$d \left(\frac{1}{40} + \frac{\log{\left(2 \right)}}{5} + \frac{\pi}{10}\right) - d \left(- \frac{11 \operatorname{atan}{\left(\frac{1}{2} \right)}}{5} - \frac{1}{5} + \frac{\log{\left(\frac{5}{4} \right)}}{5} + \frac{2 \log{\left(2 \right)}}{5}\right)$$
=
=
/1 log(2) pi\ / 1 11*atan(1/2) log(5/4) 2*log(2)\ d*|-- + ------ + --| - d*|- - - ------------ + -------- + --------| \40 5 10/ \ 5 5 5 5 /
$$d \left(\frac{1}{40} + \frac{\log{\left(2 \right)}}{5} + \frac{\pi}{10}\right) - d \left(- \frac{11 \operatorname{atan}{\left(\frac{1}{2} \right)}}{5} - \frac{1}{5} + \frac{\log{\left(\frac{5}{4} \right)}}{5} + \frac{2 \log{\left(2 \right)}}{5}\right)$$
d*(1/40 + log(2)/5 + pi/10) - d*(-1/5 - 11*atan(1/2)/5 + log(5/4)/5 + 2*log(2)/5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.