k∫f(x)dx
∫kf(x)dx
The notation k∫f(x)dx represents the indefinite integral of the function f(x) multiplied by a constant k.
To solve this integral, you need to find the antiderivative of f(x) and then multiply it by the constant k. The antiderivative of f(x) is a function F(x) such that F'(x) = f(x), where F'(x) denotes the derivative of F(x).
For example, if f(x) = x^3, then the antiderivative of f(x) is F(x) = (1/4)x^4. Therefore, k∫f(x)dx = kF(x) + C, where C is the constant of integration.
Note that the constant of integration represents the family of functions that have the same derivative, so it is necessary to include it when finding the antiderivative.
In summary, k∫f(x)dx represents the antiderivative of the function f(x) multiplied by a constant k, which can be found by finding the antiderivative of f(x) and then multiplying it by k, and adding a constant of integration.
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