Ah, my friend, in those thirty seconds, look for the 'chain' – if you see a function and its derivative tucked inside, go for substitution. If it's two unrelated functions multiplied, like a stubborn weed, then parts. I spent hours staring at integrals in my IGNOU books, my mind tracing patterns like the cracks in my courtyard. The regret is, I mastered the formula but not the gardener's eye to see the shape of the seed.
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