Please solve the following question

Asked by Balbir | 7th Oct, 2017, 11:20: PM

Expert Answer:

begin mathsize 16px style straight I equals integral straight a to the power of straight x space open square brackets logx space plus space loga space log open parentheses straight x to the power of straight x over straight e to the power of straight x close parentheses close square brackets dx straight I equals integral straight a to the power of straight x space open square brackets logx space plus space loga space open parentheses logx to the power of straight x space minus space loge to the power of straight x close parentheses close square brackets dx straight I equals integral straight a to the power of straight x space open square brackets logx space plus space loga space open parentheses xlogx space minus space straight x close parentheses close square brackets dx straight I equals integral open square brackets loga space open parentheses xlogx space minus space straight x close parentheses space plus space straight a to the power of straight x space logx close square brackets space dx For space the space integral space straight a to the power of straight x space logx space integrate space by space parts space where straight u space equals space straight a to the power of straight x space and space straight v space equals space log space straight x For space the space integral space loga space open parentheses xlogx space minus space straight x close parentheses space we space get space straight a to the power of straight x space open parentheses xlogx space minus straight x close parentheses end style

Answered by Sneha shidid | 18th Dec, 2017, 10:53: AM

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