Question

How do you integrate `int lnx/x^7` by integration by parts method?

Answer 1

We have that

#int lnx*[-x^-6/6]'dx=-1/6*lnx*x^-6+1/6*int(lnx)'*x^-6dx= -1/6*lnx*x^-6+1/6*int 1/x*x^-6dx= -1/6*lnx*x^-6+1/6*int x^-7dx= -1/6*lnx*x^-6+1/6*int (x^-6/6)'dx= -1/6*lnx*x^-6-(x^-6/36)+c= -(6*lnx+1)/(36*x^6)+c#