What to substutute to evaluate this integral? int (1+ln(x))*sqrt(1+(xlnx)^2) dx

I'm on the last problem of a maple assignment. Maple can't integrate this function. I'm trying to figure out what to substitute so that I can simplify the function into something that maple can integrate. The xlnx part is what's messing me up.

int (1+ln(x))sqrt(1+(xlnx)^2) dx

I don't need anyone to evaluate it, I just need some help figuring out what to substitute. Maple can do the rest.

Note :

∫ √(a²+u²) du = (1/2) { u·√(a²+u²) + ln | u + √(a²+u²) | } + C ... (1)
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Let : I = ∫ √[ 1 + (x· ln x)² ] • ( 1 + ln x ) dx .................. (2)
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Put : u = x· ln x

Then, by Quotient Rule,

du/dx = x·( 1/x ) + (ln x)· (1)

du/dx = 1 + ln x

( 1 + ln x ) dx = du .................................. (3)
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Using (3) in (2),

I = ∫ √(a²+u²) du.

Now Use (1).

Finally, back-substitute x·ln x for u.
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Sorry,
I should have said : Product Rule.

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