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int cos (loge x)dx is equal to...

`int cos (log_e x)dx` is equal to

A

`(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)]`

Text Solution

Verified by Experts

The correct Answer is:
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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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 02-Paper 2 (Mathematics )
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