Given ∞ 5.00 6.0⁰0 0 e ,2 du = -4² e dx = 472 xe dx = 2 [0x²e = # dx = 4x2 3 [0x³²e + dx = [²x^e=4² dx = 2 I find the exact values of the following improper integrals. sqrt(3pi)/4 3/8 3sqrt3/16 9sqrt(3pi)/64 27sqrt(3pi)/128

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A: What is Set: Set is the language of mathematics. Through set, we can define mathematical expressions…

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A: This question can be solved using the concept of integration by parts.

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A: Explanation of the answer is as follows

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A: a. I=∫(x2+5)(x-3)2xdx =∫x32+5x-12(x2-6x+9)dx =∫x72-6x52+9x32+5x32-30x12+45x-12dx…