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Question
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Solution
`intt (10x^9 + 10^x log_"e" 10)/(10^x + x^10) * "d"x`
Put 10x + x10 = u
`(10^x log_"e" 10 + 10 x^9) "d"x` = du
`int (10x^9 + 10^x log_"e" 10)/(10^x + x^10) * "d"x = int "du"/"u"`
= `log |"u" + "c"`
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10) * "d"x = log |10^x + x^10| + "c"`
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