Question:

Integrate (sin(5x))^2?

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  1. sin²(5x) = 1/2(1 - cos(10x))

    Please, finish the integration by yourself


  2. sin²(x) = 1/2 - 1/2 cos(2x)

    so sin²(5x) = 1/2 - 1/2 cos(10x)

    ∫ 1/2 - 1/2 cos(10x) dx

    = x/2 - (1/2)(1/10) sin(10x) + C

    = x/2 - (1/20)sin(10x) + C

  3. 2sin(5x)*cos(5x)
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