Please solve the following question

Asked by Balbir | 7th Oct, 2017, 11:28: PM

Expert Answer:

begin mathsize 16px style integral open parentheses log left parenthesis logx right parenthesis plus 1 over open parentheses logx close parentheses squared close parentheses dx
Put space logx space equals space straight t
rightwards double arrow straight x equals straight e to the power of straight t dt
dx equals straight e to the power of straight t dt
integral open parentheses logt plus 1 over straight t squared close parentheses straight e to the power of straight t dt
integral open parentheses logt space plus 1 over straight t space minus space 1 over straight t plus 1 over straight t squared close parentheses straight e to the power of straight t dt
integral open parentheses logt space plus 1 over straight t close parentheses straight e to the power of straight t dt minus integral open parentheses 1 over straight t minus 1 over straight t squared close parentheses straight e to the power of straight t dt
straight e to the power of straight t logt space minus space straight e to the power of straight t cross times 1 over straight t plus straight c space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses Using space integral straight e to the power of straight x open parentheses straight f left parenthesis straight x right parenthesis plus straight f apostrophe left parenthesis straight x right parenthesis close parentheses dx equals straight e to the power of straight x straight f left parenthesis straight x right parenthesis plus straight c close parentheses
xlog open parentheses logx close parentheses minus straight x over logx plus straight c end style

Answered by Sneha shidid | 21st Dec, 2017, 02:58: PM