Identification of what method to apply when solving general math problems?

Question

Good day,

I have been following single variable calculus, and I have problems solving the examination questions. Simpy said, I have difficulties with identifying what method of integration and/or differentiation to apply, to reach the desired answer.

For example:

Two examination questions

3. Determine $\int_{\pi/2}^{3\pi/2}\sin x\sin(2x)\,dx.$
4. Determine $\int \frac{x^6+1}{x^4-1}\,dx.$

I do not seek an answer to these question, more a way on how to tackle such problems, and how to identify what method to apply to solve them (substitution/partial/approximation with squeeze theorem.)

Thank you in advance.

Answer 1

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