evaluate the integral of 1/cosx(sinx)^5

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- March 11th 2009, 12:25 AMtwilightstrEvaluating integral!
evaluate the integral of 1/cosx(sinx)^5

- March 11th 2009, 05:50 AMmr fantastic
- March 12th 2009, 12:59 AMtwilightstr
however,

cosx is in the denominator - March 12th 2009, 02:04 AMADARSH
- March 12th 2009, 02:42 AMsimplependulum
1/(1-u^2)(u^5)

= (1/u)[ 1/(1-u^2)(u^4) ]

= (1/u)[ (1+u^2)/(u^4) + 1/(1-u^2) ]

= (1+u^2)/(u^5) + 1/(1-u^2)(u)

= 1/u^5 + 1/u^3 + 1/u + u/(1-u^2) - March 12th 2009, 03:52 AMchisigma
Under the assumption that the function we have to integrate is…

… the ‘standard approach’ is the change of variable…

… so that...

... and we arrive to an integral that contains rational functions and that can be solved without great difficulty. Other substitutions doesn’t work so well … at least in my opinion…

Regards