∫sinx dx =
-cosx + C
∫sin(x) dx = -cos(x) + C
where C is the constant of integration. This is because the derivative of -cos(x) is sin(x) by the chain rule of differentiation.
Alternatively, we can use integration by substitution. Let u = x, then du/dx = 1 and dx = du. Substituting these into the original integral:
∫sin(x) dx = ∫sin(u) du
Using the fact that sin(u) is the derivative of -cos(u), we have:
∫sin(x) dx = -cos(u) + C
Substituting back u = x, we get:
∫sin(x) dx = -cos(x) + C
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