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podstawiamy sinx = t, więc cosxdx = dt
∫(1-sin²x)²(cosxdx) = ∫(1-t²)²dt = ∫(t⁴-2t²+1)dt = ⅕t⁵ - ⅔t³ + t + C
podstawiamy z powrotem:
∫cos⁵xdx = ⅕sin⁵x - ⅔sin³x + sinx + C