#title:Regra de integra\c{c}\~{a}o P \frac{u'}{1-u^2}=arctanh(u)+C
#Let:



f u= [x, sin(x), cos(x), exp(x) ]; 
f du=[1, cos(x), -sin(x),exp(x) ];

u~du;



cf res = arctanh(#u);



#Question:

\noindent Calcule o integral indefinido,
$$
\int (#du)/(1-(#u)^2) dx.
$$


#Sugestion:

\noindent Utilize a f\'{o}rmula do formul\'{a}rio
$$
\int \frac{u'}{1-u^2} dx= arctanh(u)+C.
$$



#Resolution

Obtem-se
$$
\int (#du)/(1-(#u)^2) dx = #res+C.
$$

#result

$$ #res+C $$

#Verify

arctanh(#u).