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- Decide whether the given integral converges or diverges. +∞ 3 x1.5 dx 1determine whether the given integral converges or diverges. 21.∫∞1t−2et dt4. Determine whether the improper integral converges and, if so, evaluate it. (If the quantity diverges, enter DIVERGES.) ∞ 04x dx(3 + x2)2 please show step by step clearly.