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Math Help - Reduction formula

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    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.
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  2. #2
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    Quote Originally Posted by osysequeira View Post
    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.
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    Thanks

    I think your reply has shown me how to solve the problem. Thank you.
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