To integrate \( \frac{dy}{\sin x} \), we can treat \( y \) as a constant with respect to \( x \), so the problem reduces to finding the integral of \( \frac{1}{\sin x} \).

The integral of \( \frac{1}{\sin x} \) is a known standard result:

\[
\int \frac{1}{\sin x} \, dx = \ln \left| \tan \left( \frac{x}{2} \right) \right| + C
\]

Thus, the solution to your integral is:

\[
\int \frac{dy}{\sin x} = y \ln \left| \tan \left( \frac{x}{2} \right) \right| + C
\]

Let me know if you'd like a more detailed explanation, or have any further questions!

Here are five follow-up questions:
1. How would you integrate \( \frac{1}{\cos x} \)?
2. What is the integral of \( \csc^2(x) \)?
3. How does the substitution \( u = \tan(x/2) \) help in trigonometric integrals?
4. How would you evaluate \( \int \frac{dx}{\sin^2(x)} \)?
5. Can you solve the integral \( \int \frac{dx}{\tan x} \)?

**Tip**: When dealing with trigonometric integrals, it’s useful to recall identities and substitutions that simplify the integrand.

Learn how to integrate dy/ sin(x) with a detailed step-by-step solution. This problem covers key trigonometric concepts and provides the integral formula ∫ 1/ sin(x) dx = ln|tan(x/2)| + C. Suitable for students in Grades 11-12.

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