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Substitute to get t sin t, then integrate by parts (sin sqrt x and similar)

This type of question, asked 2 times: 3 May 2023 S2, 17 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    121
    The value of ∫sin⁡ ⁣x dx\int\sin\!\sqrt{x}\,dx is equal to

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  2. Question 2

    17 Apr 2026 S1

    80
    The value of ∫2x13sin⁡x23 dx\displaystyle\int 2x^{\frac{1}{3}}\sin\sqrt[3]{x^2}\,dx is

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