Saturday, May 3, 2014

`int sin(ln(x))/x dx` Evaluate the indefinite integral.

You need to use the following substitution  `ln x = t` , such that:


`ln x= t => (dx)/(x) = dt`


`int (sin(ln x))/(x) dx = int sin t dt`


`int sin t dt= - cos t + c`


Replacing back  `ln x` for t yields:


`int (sin(ln x))/(x) dx = - cos (ln x) + c`


Hence, evaluating the indefinite integral, yields` int (sin(ln x))/(x) dx = - cos (ln x) + c.`

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