Calcule a integral da função f(x)=xe^3x
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∫ x * e^(3x) dx
Método utilizado por partes
u =x ==>du=dx
e^(3x) dx = dv ==> ∫ e^(3x) dx =v ==> (1/3) * e^(3x) =v
∫ 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)- (1/3)*(1/3)* e^(3x) + const
∫ x * e^(3x) dx = (x/3)* e^(3x)-(1/9) * e^(3x) + const
∫ x * e^(3x) dx = (1/9) * e^(3x) * ( 3x -1) + const é a resposta
Método utilizado por partes
u =x ==>du=dx
e^(3x) dx = dv ==> ∫ e^(3x) dx =v ==> (1/3) * e^(3x) =v
∫ 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)- (1/3)*(1/3)* e^(3x) + const
∫ x * e^(3x) dx = (x/3)* e^(3x)-(1/9) * e^(3x) + const
∫ x * e^(3x) dx = (1/9) * e^(3x) * ( 3x -1) + const é a resposta
vanessalitiziane:
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