" 10."e^(1-x^(2))" on "[-1,1]

" *10."int e^(x)((1)/(x)-(1)/(x^(2)))dx

If y=tan^(-1)((2)/(e^(-x)-e^(x)))" then "(1+e^(2x))y_(1)=

The value of lim_(x rarr0)((e^(1/x^(2))-1)/(e^(1/x^(2)+1))) is :

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)) .

Discuss the continuity of the function f(x)={(e^((1)/(x-1)-2))/(e^((1)/(x+1)+2)),x!=1 and 1,x=1

int2/((e^x+e^(-x))^2)\ dx (a) ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x))+C (c) (-1)/((e^x+1)^2)+C (d) 1/(e^x-e^(-x))+C

Suppose f:R rarr R is a function given by f(x)={1e^(x^((10)-1))+(x-1)^(2)sin((1)/(x-1)) if x=1, if x!=1

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