Integration by Reduction Formulae

Thread starter saladfinger16
Start date Dec 15, 2010
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Formulae Integration Reduction

Dec 15, 2010

saladfinger16

Can anyone help me out with a proof for the integral that's in the attached images, its driving me nuts

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Dec 15, 2010

snipez90

You could try the trig substitution x = a*tan(u).

Or note that

\int\frac{dx}{(x^2 + a^2)^n} = \int\frac{dx}{(x^2 + a^2)^{n-1}} - \int\frac{x^2 + a^2 - 1}{(x^2 + a^2)^n}\,dx

and try to work out the last integral on the right.

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