Q21. Evaluate 10/(x-1)(x+9)Q22. Construct the reduction for integrate sin^n x dx and use it to evaluate integrate sin^6 x dxQ23. Given y ^ (1 / m) + y ^ (- 1 / m) = 2x show that (x 1) n+2 + (2n + 1)xYn+1 + (n - m)yn = 0. Q24.(a). Use the inverse function theorem to find the derivative g(x)=tan^ -1 x^ 2 .Q24. (b). Find the derivative of the inverse function of y=x^ 2 +2x+1.

10 Q21. Evaluate J (x-1) (x2+9) Q22. Construct the reduction for J sin"x dx and use it to evaluate S sin x dx. Q23. Given y1/m + y-1/m = 2x, show that (x2 - 1) yn+2 + (2n + 1)xyn+1 + (n2 - m2)yn= 0. Q24.(a). Use the inverse function theorem to find the derivative g(x) = tan-1x2. Q24.(b). Find the derivative of the inverse function of y = x + 2x + 1