How do you solve indefinite integrals?

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How do you solve indefinite integrals?

Calculus1
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Get antiderivative, +C.
You can think of indefinite integrals as just a notation convenience. The symbol \[\int f(x) dx\] is shorthand for the question " What are all of the antiderivatives for the function f(x)." There is a theorem that tells us that all the antiderivatives of a function only differ by a constant (this is where the " +C " comes from). So to represent the entire family of antiderivatives for f(x), we just need to find one antiderivative F(x) and then by this theorem every other antiderivative must take the form F(x)+C. So solving indefinite integrals only involves finding an antiderivative, and then adding the +C at the end, as Lollylau so succinctly put. Keep in mind an antiderivative of f(x) is any function F(x) such that F'(x)=f(x). For example, F(x)=sin(x) and F'(x)=cos(x). Therefore, sin(x) is an antiderivative of cos(x). I.e\[\int \cos(x) dx = \sin(x) +C\]

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