#title:Regra de integra\c{c}\~{a}o para ($\alfa \neq -1$)
#Let:


f alfa = [ 2 ,3, 4] ;
f P= [x, sin(x), cos(x), exp(x) ]; 
f dp=[1, cos(x), -sin(x),exp(x) ];

p~dp;

cf p_alfa= #p^(#alfa);
cf res = ((#p)^(#alfa+1))/(#alfa+1);



#Question:

\noindent Calcule o integral indefinido,
$$
\int (#p^(#alfa))*(#dp) dx.
$$


#Sugestion:

\noindent Utilize a f\'{o}rmula do formul\'{a}rio
$$
\int u^{\alpha} u'= \frac{u^{\alpha+1}}{\alpha+1}+C.
$$
certificando-se que $\alpha \neq 1$.


#Resolution

Obtem-se
$$
\int (#p^(#alfa))*(#dp) dx= #res+C.
$$

#result

$$ #res+C $$

#Verify

(#P^(#alfa+1))/(#alfa+1).