Question: Let I = 1 0 x p ln x dx. (a) Show that I diverges for p = 1. (b) Show that if p

Let I =∫10 xp ln x dx.
(a) Show that I diverges for p = −1.
(b) Show that if p ≠ −1, then

[xnxdx=(x-)+c XP+1 In p+1 1 p+1) +C

(c) Use L’Hôpital’s Rule to show that I converges if p > −1 and diverges if p

[xnxdx=(x-)+c XP+1 In p+1 1 p+1) +C

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