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recurrence formula (1 Viewer)

tutor01

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Given I_n = integral of x^n divided by sqrt(x^2-a^2) dx show that

nI_n - (n-1)a^2I_(n-2)=x^(n-1)sqrt(x^2-a^2).

I can't prove it. Can anyone help. Note I_n means I then subscript n like for recurrence integral questions.

Thanks!
 

tutor01

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Brilliant. I got to line 4 but did not then multiply by the root x^2-a^2 on itself. Thanks a lot.
 
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You can also do this question by splitting and then doing the +a^2-a^2 trick inside the x^2 bracket.
 

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