NEED HELP WITH ADDITIONAL MATHEMATICS

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3x+c=x^2+9x+k
x^2+6x+k=0
as line is tangent b^2-4ac=0
6^2-(4*1*k-c)
36-4k+3c=0
4k=36+4c
k=9+c
 
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what about question number 4 or 5, the one about d/dx of x^2lnx, hence

⌡ xlnx dx???
 
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