Question

\[\int\limits xsin(6x)~dx =\]a) -xcos(6x) + sin(6x) +C
b) -(x/6)cos(6x) + (1/36)sin(6x) + C
c) -(x/6)cos(6x) + (1/6)sin(6x) + C
d) (x/6)cos(6x) + (1/36)sin(6x) + C
e) 6x sin(6x) - sin(6x) + C

Answer 1

Could someone check my work pwease? :3

u = x v = -(1/6)cos(6x)
du = dx dv = sin(6x) dx
uv - ∫v du
-(1/6)x cos(6x) + (1/6)∫cos(6x) dx
-(1/6)x cos(6x) + (1/6)((1/6)sin(6x)) + C
-(x/6) cos(6x) + (1/36)sin(6x) + C

so B ?

Answer 2

Yep. Seems right to me

Answer 3

c:

Answer 4

Alright, thank you! :)

Answer 5

Good work! :)