How to solve these 2 question?

1.

7 If In tan"(x) dac, evaluate O . 10 = . 11= Now use the reduction formula In = _ - In-2 for n > 2 to evaluate . 16 = . 17 =Let's find a reduction formula for the indefinite integral In = sec" (x) dac . 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'v dx with u = tan(x) and v = tan(x) sec-2 (ac). This gives . [uv] = & and . uv = Hence, without further integration we have the reduction formula In 1 n- 1 sec-2 (x) tan(x) + g(n) In-2 where g ( n) = Use this to evaluate 14 = DO +C Recall the Maple syntax for sin (a) is sin(x)^2