Concept:Integrating each trigonometric term separately using standard formulas.Explanation:Recall that ∫cos(ax)dx=a1sin(ax)+k.Also, ∫sin(ax)dx=−a1cos(ax)+k.Apply these to the given integral:∫(cos4x+sin3x)dx=∫cos4xdx+∫sin3xdx.For cos4x, a=4, so the integral is 41sin4x.For sin3x, a=3, so the integral is −31cos3x.Add the constant of integration k.Thus, the result is 41sin4x−31cos3x+k.Answer:41sin4x−31cos3x+kThis matches option C.