# Reduction formula

• November 25th 2009, 08:25 PM
osysequeira
Reduction formula
By writing tan^n x as tan^(n-2).(sec^2 x - 1) obtain a reduction formula for Integral tan^n x dx.
• November 26th 2009, 02:08 AM
mr fantastic
Quote:

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

$I_n = \int \tan^n x \, dx = \int \tan^{n-2} x \cdot (\sec^2 x - 1) \, dx$

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

therefore

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

and you're expected to be able to solve the integral.
• November 26th 2009, 02:26 AM
osysequeira
Thanks
I think your reply has shown me how to solve the problem. Thank you.