By writing tan^n x as tan^(n-2).(sec^2 x - 1) obtain a reduction formula for Integral tan^n x dx.

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- Nov 25th 2009, 08:25 PMosysequeiraReduction formula
By writing tan^n x as tan^(n-2).(sec^2 x - 1) obtain a reduction formula for Integral tan^n x dx.

- Nov 26th 2009, 02:08 AMmr fantastic
$\displaystyle I_n = \int \tan^n x \, dx = \int \tan^{n-2} x \cdot (\sec^2 x - 1) \, dx$

$\displaystyle = \int \tan^{n-2} x \cdot \sec^2 x \, dx - \int \tan^{n-2} x \, dx$

therefore

$\displaystyle I_n = \int \tan^{n-2} x \sec^2 x \, dx - I_{n - 2}$

and you're expected to be able to solve the integral. - Nov 26th 2009, 02:26 AMosysequeiraThanks
I think your reply has shown me how to solve the problem. Thank you.