Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \), then the value of \( 2 I_{n}+n ...

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Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \), then the value of \( 2 I_{n}+n I_{n-1} \) equals to :
(a) 0
(b) \( 2 e^{2} \)
(c) \( e^{2} \)
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