I am not sure if this is the right place to ask such a question! Please let me know if this is not!
I am going to make a test for the students of Calculus 1 at the university. The test contain 4 questions and will remain open for three days. The students need to solve the questions on paper and send me a photo of their solutions. When a student opens a question, he/she has one hour to solve the question, take a photo, convert to PDF and send it to me via the system. One of the questions should be about the integration techniques. I cannot give some integrals (simple or difficult) and ask them to solve it because anyone may use some available applications or websites (like symbolab) to find the solutions.
Anyone have any idea on what sort of questions I can ask on the integration's techniques in the test.
Any help is very welcome and appreciated in advance!
An idea of mine is to give the integral
$$ \int \frac{x}{x^2-1}dx$$ and ask them to solve the integral using three different techniques!
If it's Calculus 1, the AP Calculus AB (or BC) exams have Free Response Questions (FRQs). These FRQs are usually application-based, and justification or work is required for full credit. I don't know whether you would want to grade the justification or work shown, but it definitely prevents cheating using online solvers. Although there are sections that require a graphing calculator, these sections can be removed. Also, I would switch some of the numbers and/or formatting to prevent students from simply looking up answers to the AP Calculus FRQs.
As for integration techniques, for Calculus 1, I would limit the techniques to simpler ones, (u-substitution, integration by parts, trigonometric substitution, etc.), but it may be possible to allow for multiple steps requiring different techniques to solve. One simple example:
$$\int \frac {4x-2} {3x^2+4} dx$$