Evaluate: `intsin^2(logx)dx`

Answer

`(1)/(10)x(5-2sin(2logx)-cos(2logx))+C`

Explanation

`I=int sin^(2)(logx)dx`
` "Let "t=log x " or "dt=(dx)/(x)`
`"or " dx=e^(t)dt`
`:. I=int e^(t) sin^(2)t dt=(1)/(2)int e^(t)(1-cos2t)dt`
`"or "2I=e^(t)-int e^(t)cos2t dt`
`= e^(t)-(e^(t))/(5)(2sin2t+cos2t)+C`
`"or " I=(1)/(10)x(5-2sin(2logx)-cos(2logx))+C`