Question

Marque a alternativa que corresponde ao valor da Integral Indefinida f t e^3t dt .

a) I = e^3t (t/6 - 2/3) + C

b) I = e^3t (t/6 - 1/9) + C

c) I = e^3t (t/3 + 2/9) + C

d) I = e^3t (t/5 - 1/6) + C

e) I = e^3t (t/3 - 1/9) + C

Answer 1

Boa tarde

I = ∫ t e^(3t) dt 

∫ f dg = fg - ∫ g df 

f = t , df = dt
dg = e^3t dt , g = 1/3 e^3t

∫ t e^(3t) dt  = t*e^3t/3 - e^3t/9 + C

∫ t e^(3t) dt = 1/9 * e^3t (3t - 1) + C