The integral of cos(x) can be evaluated using integration by substitution:
Let u = sin(x); then du/dx = cos(x) and dx = du/cos(x)
Substituting for dx and cos(x), we have:
∫cosx dx = ∫1 du/u (since cos(x) = 1/sin(x) when u = sin(x))
= ln|u| + C (where C is the constant of integration)
= ln|sin(x)| + C (substituting u back in)
Therefore, the antiderivative of cos(x) is ln|sin(x)| + C.
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