" 2.(i) "e^(2/x)

Integrate the following with respect to x. (i) (e^(2x) - 1)/(e^x) " " (ii) e^(3x)(e^(2x - 1)) .

" (i) "int e^(x)[e^(log x)+2]dx

Evaluate: (i) int(e^(2x))/(e^(2x)-2)\ dx

Integrate the following with respect to x. (i) e^(ax)cosbx (ii) e^(2x)sinx (iii) e^(-x)cos2x

Prove that , the minimum value of (i) 4e^(2x)+9e^(-2x)" is "12 , (ii) (x)/(logx) is e.

Evaluate: (i) intx\ e^x^2\ dx (ii) int(e^(2x))/(1+e^x)\ dx

Find the number of points of intersection (i) e^(x)=x^(2),(2)log_(e)x=-x

Evaluate: (i) int xe^(x)^^2dx (ii) int(e^(2x))/(1+e^(x))dx

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

Differentiate the following (i)e^(2//x)" "(ii)e^(sqrtx)" "(iii) e^(-2sqrtx)