Resposta:
[tex]\boxed{-\cos{\big(\sin{x}\big)}+C}[/tex]
Explicação passo-a-passo:
[tex]\boxed{\int{\cos{x}\sin{\big(\sin{x}\big)dx}}}[/tex]
[tex]u=\sin{x}\ \therefore\ \dfrac{du}{dx}=\cos{x}\ \therefore\ du=\big(\cos{x}\big)dx[/tex]
[tex]\int{\cos{x}\sin{\big(\sin{x}\big)dx}}=\int{\sin{u}du}=\boxed{-\cos{u}+C}=[/tex]
[tex]=\boxed{-\cos{\big(\sin{x}\big)}+C}[/tex]
