How to integrate sec^5 x by parts ??? (1 Viewer)

coeyz · Apr 14, 2009

These are the integration by parts questions:

1.) integrate sec^5(x) dx
2.) integrate cosec^2 (sqrt x) dx

THANKS A LOT =(

coeyz · Apr 14, 2009

oh i can do the first one now =D
can anyone do the second one for me please?

Drongoski · Apr 14, 2009

Q1)

$Let\ \ I_{5}\ \ =\ \ \int sec^{5}x\ dx\ \ =\ \ \int sec^{3}x\ sec^{2}x\ dx\\ \\ \ \ =\ \ tan x\ sec^{3}x\ -\ 3\int tan x\ sec^{2}x\ (sec\ x\ tan\ x)dx\\ \\ =\ \ tan\ xsec^{3}x\ -\ \ 3\int tan^{2}x\ sec^{3}x\ dx\\ \\ = \ \ tan\ x\ sec^{3}x\ -\ 3\int (sec^{2}x\ -\ 1)sec^{3}x\ dx\\ \\ =\ \ tan\ x\ sec^{3}x\ -\ 3[I_{5}\ -\ I_{3}]\\ \\ \therefore \ \ 4I_{5}\ \ =\ \ tan\ x\ sec^{3}x\ +\ 3I_{3}\\ \\etc\ etc\ \\ \\ So \ you\ have\ a\ reduction\ formula$

Trebla · Apr 14, 2009

coeyz · Apr 17, 2009

thanks heaps guys

How to integrate sec^5 x by parts ??? (1 Viewer)

coeyz

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coeyz

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Drongoski

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Trebla

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coeyz

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