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Integrand over sin^2 x cos^2 x: split using sin^2 x + cos^2 x = 1

This type of question, asked 3 times: 26 Apr 2025 S2, 15 Apr 2026 S2, 19 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    26 Apr 2025 S2

    121
    ∫dxsin⁡2x cos⁡2x=\int\frac{dx}{\sin^{2}x\ \cos^{2}x}=

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  2. Question 2

    15 Apr 2026 S2

    79
    The value of ∫sin⁡6x+cos⁡6xsin⁡2x⋅cos⁡2x dx\displaystyle\int\dfrac{\sin^6 x + \cos^6 x}{\sin^2 x\cdot\cos^2 x}\,dx is

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  3. Question 3

    19 May 2026 S1

    82
    ∫sec⁡22x⋅csc⁡⁡22x dx=…\displaystyle\int \sec^2 2x \cdot \operatorname{\csc}^2 2x\,dx = \ldots

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