`int cos(2tan^(-1)sqrt((1-x)/(1+x)))dx" is equal to "" (A) "(1)/(8)(x^(2)-1)+C, " (B) "(x^(2))/(4)+C , " ""(C)" (x)/(2)+C ," "(D) "(x^(2))/(2)+C`

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

[" 0.",int sin^(-1)sqrt((x)/(a+x))dx" is equal to "],[," 1) "(x+a)tan^(-1)sqrt((x)/(a))-sqrt(ax)+C],[" 3) "(x+a)cot^(-1)sqrt((x)/(a))-sqrt(ax)+C," 2) "(x+a)tan^(-1)sqrt((x)/(a))+sqrt(ax)+C]

If int sqrt(1+sec x)dx=2sin^(-1)[sqrt(2)f(x)]+c then (d)/(dx)[f(x)] is equal to (A)cos(x)/(2)(B)-(1)/(2)cos(x)/(2)(C)(1)/(2)cos(x)/(2)(D)(1)/(2)sin(x)/(2)

int(x^(3)dx)/(sqrt(1+x^(2))) is equal to (A) (1)/(3)sqrt(1+x^(2))(2+x^(2))+C(B)(1)/(3)sqrt(1+x^(2))(x^(2)-1)+C(C)(1)/(3)(1+x^(2))^((3)/(2))+C(D)(1)/(3)sqrt(1+x^(2))(x^(2)-2)+C

int e^(x)((x-2)/((x-1)^(2)))dx is equal to (i) (e^(x))/(x-1)+C (ii) (e^(x))/((x-1)^(2))+C( iii) (2e^(x))/((x-1)^(2))+C( iv )(e^(x)-1)/(x-1)+C

int(x)/(4+x^(4))dx is equal to (1)/(4)tan^(-1)x^(2)(b)(1)/(4)tan^(-1)((x^(2))/(2))(c)(1)/(2)tan^(-1)((x^(2))/(2))(d) none of these

Choose the correct answer int sqrt(1+x^(2))dx is equal to (A)(x)/(2)sqrt(1+x^(2))+(1)/(2)log|(x+sqrt(x+x^(2)))|+C (B) (2)/(3)(1+x^(2))^((3)/(2))+C(C)(2)/(3)x(1+x^(2))^((3)/(2))+C(D)^(2)sqrt(1+x^(2))+(1)/(2)x^(2)log|x+sqrt(1+x^(2))|+C

If int(1)/((x^(2)+1)(x^(2)+4))dx=Atan^(-1)x+B" tan"^(-1)(x)/(2)+C , then

(d)/(dx){tan^(-1)((cos x)/(1+sin x))} equal (1)/(2)(b)x(c)(1-x^(2))/(1+x^(2)) (d) 1

If int((x+1))/(sqrt(2x-1))dx=f(x)sqrt(2x-1)+C. Then f(x) is equal to (A)(x+4)/(3) (B) (x+3)/(4) (C) (2)/(3)(x+2)(D)x+4