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∫ex[(x+3)(x+4)]dx - Mathematics and Statistics

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Question

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

Sum

Solution

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x = int "e"^x[(x + 4 - 1)/(x + 4)^2]  "d"x`

= `int "e"^x[1/(x + 4) - 1/(x + 4)^2]  "d"x`

= `"e"^x(1/(x + 4)) + "c"`    .......`[∵ int"e"^x["f"(x) + "f'"(x)]  "d"x = "e"^x*"f"(x) + "c"]`

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Chapter 2.3: Indefinite Integration - Very Short Answers

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