Identify the correct substitution (using u, du) to make in each of the following integrals. Then, compute the integral.
a) ∫ 8x(x²-3)⁷dx
b) ∫ [√cot(x)] csc²(x) dx
c) ∫ cos(x)(sin³(x)+3sin²(x)a²+a³)dx where a is some real number (Hint for C: Work smarter not harder)
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