(x^(4))((1)/(3^(4)))^(1/2)

If I=int(1+x^(4))/((1-x^(4))^((3)/(2)))dx=(1)/(sqrt(f(x)))+C (where, C is the constant of integration) and f(2)=(-15)/(4) , then the value of 2f((1)/(sqrt2)) is

If I=int(1+x^(4))/((1-x^(4))^((3)/(2)))dx=(1)/(sqrt(f(x)))+C (where, C is the constant of integration) and f(2)=(-15)/(4) , then the value of 2f((1)/(sqrt2)) is

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

lim_(x rarr a){[(a^((1)/(2))+x^((1)/(2)))/(a^((1)/(4))-x^((1)/(4))))^(-1)-(2(ax)^((1)/(4)))/(x^((3)/(4))-a^((1)/(4))x^((1)/(2))+a^((1)/(2))x^((1)/(4))-a^((3)/(4)))]^(-1)-sqrt(2)^(log_(4)a)}^(8)

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

Let 0

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]