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प्रश्न
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
उत्तर
Let I = `int(sin(logx)^2)/x.log.x.dx`
Put (logx)2 = t
∴ `2logx. 1/x.dx` = dt
∴ `1/xlogx.dx = (1)/(2)dt`
∴ I = `(1)/(2) int sin t.dt`
= `-(1)/(2) cost + c`
= `-(1)/(2)cos[(logx)^2] + c`.
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