# Integration -3

Calculus Level 5

If $$\displaystyle I_n = \int_0^1 \dfrac{(\ln x)^n }{\sqrt x} \, dx$$, then of which of the following is/are true?

Choose the most precise option.

(A): $$I_n$$ has a finite value for all positive integers $$n$$.
(B): $$\dfrac{I_2}{I_1} + \dfrac{I_3}{I_2} + \dfrac{I_4}{I_3} = -4$$.
(C): $$I_4 = -9$$.
(D): $$I_8 = 40331$$.

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