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Question
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Options
ex log x + c
ex (log x)2 + c
xex log x + c
`(e^x log x)/x + "c"`
MCQ
Fill in the Blanks
Solution
`int "e"^x/x [x (log x)^2 + 2 log x] "dx"` = ex (log x)2 + c.
Explanation:
`int "e"^x/x [(log x)^2 + (2 log x)/x] "dx"`
`= "e"^x (log x)^2 + "c" ....[because int "e"^x ["f"(x) + "f'"(x)] "dx" = "e"^x "f"(x) + "c"]`
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