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Evaluate: int1/(x^3)sin(logx)\ dx...

Evaluate: `int1/(x^3)sin(logx)\ dx`

Text Solution

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Let `I=int frac{1}{x^{3}} sin (log x) d x`
Putting `log x=t`
` Rightarrow x=e^{t} `
` Rightarrow d x=e^{t} d t `
` therefore I=int frac{1}{e^{3 t}} sin t e^{t} d t `
` =int e^{-2 t} sin t {dt}`
...
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