`int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))=` (a) `1/2ln(1+sqrt(1+x^2))+c` (b) `2sqrt(1+sqrt(1+x^2))+c` (c) `2(1+sqrt(1+x^2))+c` (d) `4sqrt(1+sqrt(1+x^2))+c`

If int(x)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))dx))=k sqrt(1+sqrt(1+x^(2))+c. find k)

int(dx)/((1+sqrt(x))sqrt((x-x^(2)))) isequa

int(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(2))sqrt(1+x^(2)))dx=

int x((ln(x+sqrt(1+x^(2))))/(sqrt(1+x^(2))))dx=a sqrt(1+x^(2))ln(x+sqrt(1+x^(2)))+bx

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

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

Solve the equations. sin(tan^(-1)x),|x|<1 (a) x/(sqrt(1-x^2)) (B) 1/(sqrt(1-x^2)) (C) 1/(sqrt(1+x^2)) (D) x/(sqrt(1+x^2))

Integrate : (a) int (sqrt(1-x^2) + sqrt(1+x^2) )/( sqrt(1-x^4) dx,

(d)/(dx)[cos^(-1)(x sqrt(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.1/4c.-1/4d none of these