" Q) "int(1)/(x^(e))sin(log x)dx" and "

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1. int(1+x)/(x*sin(x+log x))dx

int_((1)/(e))^(e)|log x|dx=

int_(1)^(e) log (x) dx=

int (e^(x))/(x)(x log x+1)dx

int e^(x) (e^(log x)+1) dx

" (i) "int e^(x)[e^(log x)+1]dx

The value of int_(1)^(e)(1)/(x)(1+log x)dx is

int_(1)^(e^(99))(sin(pi.ln x))/(x)dx=

int (1+log_e x)/x dx