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\[\int\limits x ^{4lnx dx}\]

Always remember neat trick called I L A T E

For this problem I would first do U-subtitution

Did it help?

I think he meant:
\[\int\limits\limits_{}^{}(x^4)(Lnx)dx\]

Let u = Lnx; du = (1/x)dx; dv = x^4; v = x^5/5