Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \). Then answer the following quest....

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Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \). Then answer the
\( \mathrm{P} \)
following questions.
W
\( 2 I_{n}+n I_{n-1} \) is equal to
(1) 0
(2) \( 2 e^{2} \)
(3) \( e^{2} \)
(4) 1


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