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# Indefinite integral

Indefinite integration 不定积分

Anti-derivative 导数反向

Antiderivative is the reverse relation of derivative.

For example, we know that the derivative of $$x^2$$ is $$2x$$. This means that an antiderivative of $$2x$$ is $$x^2$$.

Solving indefinite integral formula is kind of like do anti-derivative.

The indefinite integral of $$2x$$ is expressed as $$\int 2x dx$$

In general,

$$\int f^\prime(x) dx = f(x) + C$$

or

$$\int \frac{dy}{dx} dx = dy + C$$

$$\int \frac{dy}{dx} dx = \int dy$$ means infinite $$dy$$.

Here $$dy$$ actually is the original function $$f(x)$$.

If we want to make it infinite, we should add or minus a number to it, we call that number `C`. Finally we got $$\int dy = dy + C$$

One thing you should know is that $$dy + C$$ means so many many $$f(x)$$ which composed with $$dy$$ adding or subtracting a unknown random number $$C$$