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 $C$