1.

`int cos (log_e x)dx` is equal toA. `(1)/(2)xx[cos(log_ex)+sin(log_ex)]`B. `(x)[cos(log_e x)+sin(log_ex)]`C. `(1)/(2)x[cos(log_e x)-sin(log_e x)]`D. `x[cos (log_ex)-sin(log_ex)]`

Answer» Correct Answer - A
Let `l=intcos(log_ex)dx`
`=cos(log_eX)x-int((-sinlog_ex)/x)xdx`
`= x cos (log_ex)+int sin(log_ex).1dx`
`=xcos(log_ex)+xsin(log_ex)-int(cos(log_ex))/(x)x dx`
`=xcos(log_ex)+ xsin(log_ex)-l`
`rArr 2l=x[cosIog_ex)+sin(log_ex)]`
`rArr l=(x)/(2)[cos(log_ex)+sin(log_ex)]`


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