`cos^(3)xe^(logsinx)`

Explanation

माना
`I=intcos^(3)xe^(logsinx)dx=int(cosx)^(3)sinx dx`
`" "(because e^(logx)=x)`
`=-int(cosx)^(3)(-sinx)dx`
माना `cosx=t" "rArr" "-sinxdx=dt`
`therefore" "I=-int t^(3)dt=-(t^(4))/(4)+C=-(cos^(4)x)/(4)+C`