21.(e^(x)(x^(2)+1))/((1+x)^(2))

int_(1)^(2)((x^(2)-1)/(x^(2)))e^(x+(1)/(x))dx=e^((5)/(2))-e^(2)

f(x)=(e^(2x)-1)/(e^(2x)+1) is

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

If x - (1)/( x) = sqrt21, then the value of (x ^(2) + (1)/( x ^(2))) (x + (1)/(x)) is

If y = (e^(x)-e^(-x))/(e^(x)+e^(-x)) then prove that y = (e^(2x)-1)/(e^(2x)+1) .

int e^(x)((x-2)/((x-1)^(2)))dx is equal to (i) (e^(x))/(x-1)+C (ii) (e^(x))/((x-1)^(2))+C( iii) (2e^(x))/((x-1)^(2))+C( iv )(e^(x)-1)/(x-1)+C

int_(1)^(2)((1)/(x)-(1)/(x^(2)))e^(x)dx=e((e)/(2)-1)

int_(1)^(2)((1)/(x)-(1)/(x^(2)))e^(x)dx=e((e)/(2)-1)

If (x-(1)/(x))=sqrt(21), the value of (x^(2)+(1)/(x^(2)))(x+(1)/(x)) is (a) 42(b)63(c)115 (d) 120(e)125