Final answer:
The integral of -5sinx with respect to x is 5cosx + C, where C is the constant of integration.
Step-by-step explanation:
When we evaluate the integral ∫(-5sinx) dx, we are looking for an antiderivative of the function -5sinx. The antiderivative of sinx is -cosx, so when we incorporate the coefficient -5, we have -5(-cosx), which simplifies to 5cosx. Therefore, the integral of -5sinx with respect to x is:
∫(-5sinx) dx = -5∫sinx dx = -5(-cosx) + C = 5cosx + C,
where C represents the constant of integration.