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(Solved): Need complete solution including all steps. solve the given integrals when n is odd and even seperat ...



Need complete solution including all steps.
solve the given integrals when n is odd and even seperately.

Calculate the integral.
\[
I_{n}=\int_{0}^{\infty} x^{n} e^{-a x^{2}} d x \text { where }
\]
Calculate the integral.


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The answer provided below has been developed in a clear step by step manner.


Let's consider the integral where n can be odd or even.

Case 1: n is odd
Assume n=2m+1 for some integer m.
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