(x sqrt(1+x))/((1+x^(2))^(3/2))

Find (dy)/(dx) , when: y=(x^(2)sqrt(1+x))/((1+x^(2))^(3//2))

Simpify : (1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3))/(1-3((1-x^2)/(x^2)))}^2 .

Evaluate {:(" Lt"),(xrarr1):}((2x-1)(sqrt(x)-1))/((2x^(2)+x-3))

If quad cos^(-1)[x^((4)/(3))-sqrt((1-x^(2))(1-x^((2)/(3)))),0<=x<=1, find (dy)/(dx)

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

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

sqrt((1)/(x^(2))-(3)/(x))<(1)/(x)-(1)/(2)

(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

int(x^(3))/(sqrt(1+x^(2)))dx=a(1+x^(2))^((3)/(2))+b* sqrt(1+x^(2))+C