Answer:sin(sin(x)) + C.
Step-by-step explanation:
To integrate sin(x)cos(sinx), we can use the substitution u = sin(x). Then, du/dx = cos(x) and dx = du/cos(x). Substituting these values, we get:
∫sin(x)cos(sinx)dx
= ∫cos(u)du
= sin(u) + C
= sin(sin(x)) + C
Therefore, the integration of sin(x)cos(sinx) is sin(sin(x)) + C.
