Today I saw a book in the bookstore that has the following integral on its cover:
$$\int \frac {dx}{dx} = \frac {1}{d} \ln x + c$$
I don't understand the meaning of $\frac {1}{d}$. Also, $\frac {dx}{dx}$ looks odd to me. Can someone please explain these notations to me? I think these notations may be valid, because the author is very famous in my country.
If this is a valid integral, can someone also tell me how to solve integrations that has more than one differentials? By "differential", I mean $dx$, $dy$, $du$, etc. For example:
$$\int \frac {u \cdot dx^2}{du^2} \tag 1 $$
P.S. The above integral is actually:
$$\int \frac {\sin(x)}{\cos^2(x)}dx \tag 2 $$
If you try to solve (2) by a variable change of $u = \sin(x)$, the outcome would be (1) (I know that (1) can be easily solved by getting $\cos^2(x)$ as $u$). But I want to know that if (2) has also an answer.