Question

Qual é o alor da integral indefinida (x+2) cos3x dx

a) (x^2)/2 + x + sen3x + c
b) (x + 2) sen3x + cos3x + c
c) ((x + 2) sen3x) / 3 + (cos3x) / 9 + c
d) (x + 2) sen3x - cos3x + c
e) ((x + 2) sen3x) / 3 - (cos3x) / 9 + c

Answer 1

 ∫ (x+2)cos(3x) dx 
u= x+2       dv= cos(3x)dx
du = dx       v = (1/3) * sen(3x)

 ∫ udv = uv -  ∫ vdu 
(x+2)*(1/3) * sen(3x) -  ∫ (1/3)*sen(3x)dx 
(x+2)*(1/3)*sen(3x) - (1/3) * (-(1/3)*cos(3x)) + c 
(x+2)*(1/3)*sen(3x) + (1/9)*cos(3x)  + c 

LETRA C