Substitution in integral

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Hi members,

see attached Pdf file.
For a<0,write b=-a and let x=bt.Then

My question:

how becomes the denominator x+a to 1-t??? I don't see it

Thank you
 

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  • #2
HallsofIvy
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The integral is
[tex]\int_0^\infty \frac{x^{\mu-1}dx}{x+ a}[/tex]

You attachment says "if a< 0 let b= -a" so becomes
[tex]\int_0^\infty \frac{x^{\mu-1}dx}{x- b}[/tex]

and "let x= bt". The denominator is x- b= bt- b= b(t- 1)

Factor out "-b" leave 1- t in the denominator,
 

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