`int(1+x+sqrt(x+x^2))/(sqrt(x)+sqrt(1+x))dxi se q u a lto` `1/2sqrt(1+x)C` (b) `2/3(1+x)^(x/2)+C` `sqrt(1+x)+c` (d) `3/2(1+x)^(3/2)+C`

int frac {1+x+sqrt (x+x^2)}{sqrt x + sqrt (1+x)} dx = .......... A) (1/2) sqrt (x+1) +c B) 2/3 (x+1)^(3/2) +c C) sqrt (x+1) +c D) 2 (x+1)^(3/2) +c

int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto (sqrt(e))/2(sqrt(3)+1) (b) (sqrt(3e))/2 sqrt(3e) (d) sqrt(e/3)

The value of integral inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi se q u a lto e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c none of these

int (dx)/((x + 1) sqrt(x)) is equal to a) tan^(-1) sqrt(x) + C b) 2 tan^(-1) x + C c) 2 tan^(-1) (sqrt(x)) + C d) tan^(-1) (x^((3)/(2))) + C

int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3sqrt(1+x^2)(x^2-1)+C 1/3(1+x^2)^(3/2)+C (d) 1/3sqrt(1+x^2)(x^2-2)+C

int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3sqrt(1+x^2)(x^2-1)+C 1/3(1+x^2)^(3/2)+C (d) 1/3sqrt(1+x^2)(x^2-2)+C

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dxi se q u a lto e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c none of these

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e nai se q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3