cosx dx
sinx + c
The integral of cosx dx simply evaluates to sinx + C, where C is the constant of integration. To understand why, we can use integration by substitution:
Let u = x, then du = dx. Thus, we can rewrite the integral as:
∫ cosx dx = ∫ cos(u) du
Integrating the new expression, we get:
∫ cos(u) du = sin(u) + C
Finally, substituting back u = x, we get:
∫ cosx dx = sinx + C
Therefore, the antiderivative of cosx is sinx plus a constant added for the indefinite integral of the function.
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