`intsinxlog(cosx)dx=?`

Options

A. `cosxlog(cosx)-cosx+C`
B. `-cosxlog(cosx)+cosx+C`
C. `cosxlog(cosx)+cosx+C`
D. none of these

Answer

B

Explanation

Put cos x=t and - sin x dx=dt.
`:." "I=-intlogtdt=-int(underset(I)(logt)*underset(II)1)dt=-{:[(logt)t-int(1)/(t)*tdt]:}`
`=-t(logt)+t+C=-cost[log(cost)]+cosx+C`.