sinx dx
-cosx + c
The integral of sinx with respect to x is -cosx + C, where C is a constant of integration.
To understand how we arrived at this result, we can use integration by substitution. Let u = cosx, then du/dx = -sinx. Rearranging, we get -du = sinx dx.
Substituting -du for sinx dx, we can rewrite the original integral as ∫-du, which evaluates to -u + C. Substituting back u = cosx, we get -cosx + C as the final answer.
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