Evaluate:`intsin^2(logx)dx`

1.	Evaluate:`intsin^2(logx)dx`
Answer» Correct Answer - `(1)/(10)x(5-2sin(2logx)-cos(2logx))+C` `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`

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