We note that (2-1)3/2 (x-1). Expression = Therefore, the following entry from the Table of Trigonometric Substitutions is appropriate. Substitution Identity x = a sec(6), 0 8 < or 8 < 2 2 sec2(0)-1=tan2(e) If if (x-1) = (x-a), then a = 1 Therefore, we can let x = sec(0), so dx = sec(0)tan (0) tan(0) sec()) de. We also must make a substitution for the limits of integration in the definite integral. Since x = sec(0), we note that when x = 2,0 = 3 Step 2 We have determined that if we let x = sec(8), then dx = sec(0) tan(e) de on the interval dx (x - 13/2 = 1/30 sec (4) sec(8) tan(6) tan(0) de Further, when x = 4,8 = sec == 3 sec (4)]. Applying the substitution gives us the following result. To evaluate this trigonometric integral, we put everything in terms of sin(e) and cos(0). Doing so gives the following result. sec (4) sec(0) tan(6) tan (0) sec (4) de= Submit Skip (you cannot come back) cos(6) de