((1)/(2))^(x^(6)-2x^(4))<2^(x^(2))

solve : (5x+1)/(2)-(x-2)/(6)=(2x+4)/(3)

(x^(2)+(1)/(x^(2))+2)+(x^(4)+(1)/(x^(4))+5)+(x^(6)+(1)/(x^(6))+8)+

If int(x^(6)+x^(4)+x^(2))(2x^(4)+3x^(2)+6)^(1//2)dx=k(Ax^(6)+Bx^(4)+Cx^(2))^(p)+C_(1) then

If "int(x^(2)+2x^(4)+3x^(6))(1+x^(2)+x^(4))^(1/2)dx=k(Ax^(2)+Bx^(4)+cx^(6))^(p)+l then

Simplify : ((1)/(2)x(1)/(4))+((1)/(2)x6)

Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2y)^(5) (iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5) (v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)

1-(x^(2))/(2!)+(x^(4))/(4!)-(x^(6))/(6!)+....=

int((x^(- 6)-64)/(4+2x^(- 1)+x^(- 2))*(x^2)/(4-4x^(- 1)+x^(- 2))-(4x^2(2x+1))/(1-2x))dx

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)-...]