Question

A alternativa que corresponde à solução de
∫ 5xe ^(3x) dx
é:

Answer 1

Resposta:

∫ 5x * e^(3x) dx

fazendo por partes

u =x  ==> du=dx e^(3x) dx

dv = e^(3x) dx  ==>∫ dv =∫  e^(3x) dx  ==>v= (1/3)* e^(3x)

∫ x * e^(3x) dx  = (x/3)* e^(3x) - ∫  (1/3)* e^(3x) dx

∫ x * e^(3x) dx  = (x/3)* e^(3x) -(1/3)* ∫   e^(3x) dx

∫ x * e^(3x) dx  = (x/3)* e^(3x) -(1/9)*   e^(3x)  + c

∫ 5x * e^(3x) dx  = (5x/3)* e^(3x) -(5/9)*   e^(3x)  + c  

∫ 5x * e^(3x) dx  = (5/9)* 3x*e^(3x) -(5/9)*   e^(3x)  + c  

∫ 5x * e^(3x) dx  = (5/9)*e^(3x) * (3x-1) + c

∫ 5x * e^(3x) dx  = (5/3)*e^(3x) * (x-1/3) + c