`intdx/(sqrt(x)(1+x^2)^(5/4))=`
(A) `(2x)/(1+x^2)^(1/4)+c` (B) `(2sqrt(x))/(1+x^2)^(1/4)+c` (C) `(2sqrt(x))/(1+x^2)+c` (D) none of these

intdx/(x^2sqrt(x^2-1))

intdx/((x-1)^(3/4)(x+2)^(5/4))= (A) 4/3((x-1)/(x+2))^(1/4)+c (B) 4/3sqrt((x-1)/(x+2))+c (C) 4/3((x+2)/(x-1))^(1/4)+c (D) none of these

intdx/((x-1)sqrt(x^2-1))

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (sqrt(x^4+x^2+1))/(x^2)+C (c) (sqrt(x^4+x^2+1))/x+C (d) none of these

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

The solution of (1-x^2) dy/dx+2xy-xsqrt(1-x^2)=0 , is (A) y/((1-x^2))=1/sqrt(1-x^2)+C (B) y(1-x^2)=sqrt(1-x^2)+C (C) y(1-x^2)^(3/2)=sqrt(1-x^2)+C (D) none of these

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dx is equal to (a)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^3)))+c (b)e^x(1/(sqrt(1+x^2))-x/(sqrt((1+x^2)^3)))+c (c)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^5)))+c (d)none of these

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

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

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these