Question

O valor da integral indefinida R
x cos xdx ´e:
(a) x + sin x + C
(b) x sin x + cos x + C
(c) x sin x + x
2 + C
(d) x sin x + cos x
2 + C
(e) x
2
sin x + cos x + C

Answer 1

Resposta:

(b) xsin(x) + cos(x) + C

Explicação passo a passo:

$\int{xcos(x)}\,dx$

u = x ⇒ du = dx

dv = cos(x) dx ⇒ v = sin(x)

$\int{u}\,dv=uv-\int{v}\,du\\\\\int{xcos(x)}\,dx=xsin(x)-\int{sin(x)}\,dx\\\\\int{xcos(x)}\,dx=xsin(x)-(-cos(x))+C\\\\\int{xcos(x)}\,dx=xsin(x)+cos(x)+C$