Evaluate : `intx^(n)logxdx`.

1.	Evaluate : `intx^(n)logxdx`.
Answer» (i) Integrating by parts, taking x as the first function, we get `intx^(n)logx=(logx)intx^(n)dx-int{(d)/(dx)(logx)intx^(n)dx}dx` `=(logx)(x^(n+1))/((n+1))-int(1)/(x)(x^(n+1))/((n+1))dx` `=(x^(n+1)logx)/((n-1))-(1)/((n+1))intx^(n)dx` `=(x^(n+1)logx)/((n-1))-(x^(n+1))/((n+1)^(2))+C`.

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