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Question

x+12 ex dx

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Solution

x+12I exII dx=x+12ex dx-ddxx+12exdxdx=x+12·ex-2 x+1·ex dx=x+12 ex-2xI exII dx-2ex dx=x+12 ex-2 x·ex-1·ex dx-2ex=x+12 ex-2x ex+2ex-2ex+C=x+12-2x ex+C=x2+1 ex+C

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