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Question

Let $I_{n}(x)=\int_{0}^{x} \frac{1}{\left(t^{2}+5\right)^{n}} d t, n=1,2,3, \ldots .$ Then :

$50 I_{6}-9 I_{5}=x I_{5}^{\prime}$
$50 I_{6}-11 I_{5}=x I_{5}^{\prime}$
$50 I_{6}-9 I_{5}=I_{5}^{\prime}$
$50 I_{6}-11 I_{5}=I_{5}^{\prime}$

Solution

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