[" 24244तl "((e^(x)-1)(2x-3)(x^(2)+x+2))/((sin x-2)(x+1)^(2)x)<=0],[" -il "6}G]

Solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sin x-2)(x+1)^(2)x)<=0 is

lim_(x rarr0)(e^(x)-1-sin x-(tan^(2)x)/(2))/(x^(3))

lim_(x to 0)(e^(2x)-1)/(sin 3x) = ?

lim_(x rarr0)(2e^(sin x)-e^(-sin x)-1)/(x^(2)+2x)

int e^(x)(1-sin x)/(1+sin x)=-e^(x)cot((x)/(2))+c

int(2e^(5x)+e^(4x)-4e^(3x)+4e^(2x)+2e^(x))/((e^(2x)+4)(e^(2x)-1)^(2))dx= a) "tan"^(-1)(e^(x))/(2)-(1)/(e^(2x)-1)+C b) "tan"^(-1)e^(x)-(1)/(2(e^(2x)-1))+C c) "tan"^(-1)(e^(x))/(2)-(1)/(2(e^(2x)-1))+C d) 1-"tan"^(-1)((e^(x))/(2))+(1)/(2(e^(2x)-1))+C

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

(2+sin 2x)/(1+cos 2x) e^(x)

(2+sin 2x)/(1+cos 2x) e^(x)