Let's say I wrote an integral in equation (1) for instance. Is the following sentence has grammatical errors in the perspective of mathematics and english language:
" Substituting $x^{2} = t \rightarrow 2x \, dx = dt $ then $t = y^3 \rightarrow dt = 3y^2 \, dy $ in the integral in equation (2), gives... "
If the question is not suitible for this site, ı will immediately delete the question in the direction of your comments. Thank you!
An arrow, $\text{“}\longrightarrow\text{''}$ is used in calculus in such statements as $f(x) \to L$ as $x\to a.$
It is used in many mathematical contexts, where $P\longrightarrow Q$ means "If $P$ then $Q.$"
And it is used in things like $f:A\to B.$
And it's probably used in some other commonplace contexts that are not occurring to me just now.
It is also used by confused students to mean something like "The next step after that is..." or as a catch-all when they don't know what else to use.
I wouldn't use it in the way in which you've used it.
I might write:
"Substituting $x^2 = t,$ so that $2x\,dx = dt,$ and also $t=y^3,$ so that $dt = 3y^2\,dy$, in equation $(2),$ gives..."