Let's find a reduction formula for the indefinite integral In = sec" (x) da . If n > 2 then we can rewrite this integral as In = (1+ tan?(x)) sec"-2(x) da = In-2 + /tan?(x) sec-2(x) da. Now use integration by parts to get tan?(x) sec-2(x) da = uv' dx = [uv] - u'vdx with u = tan(x ) and v = tan(x) sec-2(x). This gives . [uv] = DOand . UV = Hence, without further integration we have the reduction formula In = = n-1 sec-2 (x) tan(x) + g(n) In-2 where g(n) = Use this to evaluate 14 = AD +C Recall the Maple syntax for sin (a) is sin(x) ^2