Evaluate: `intlogx(sin{1+(logx)^2})/xdx`

Explanation

We have given,

`intlogx(sin{1+(logx)^2})/xdx`

Let `t=(log x)^(2)`

`implies dt=(2log x)/(x)dx`

As we know` ((f(g(x)))^(')=g^(')(x)f^(')(g(x))),`

` int log x(sin(1+(log x)^(2)))/(x)dx`

`=int sin(1+(log x)^(2))xx(log x)/(x)dx,`

`=int sin(1+t)xx(dt)/(2),`

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