`int((x^(2)+1)e^(x))/((x+1)^(2))dx`

If int_(0)^(1) (e^(x))/( 1+x) dx = k , then int_(0)^(1) (e^(x))/( (1+x)^(2)) dx is equal to

Find (i) inte^x(t a n^(-1)x+1/(1+x^2))dx (ii) int((x^2+1)e^x)/((1+x)^2))dx

int_(0)^(2) (e^(-1//x))/(x^(2)) dx

int((1-x)e^(x))/(x^(2))dx

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

int(x e^(2x))/((1+2x)^2)dx

Evaluate the following: (i) int(sec^(2)x)/(3+tanx)dx " (ii) " int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx (iii) int(1-tanx)/(1+tanx)dx " (iv) " int(1)/(1+e^(-x))dx

Evaluate int((x^2+1)e^x)/(x+1)^2dx

STATEMENT-1 : int(x^(2)-1)/(x^(2))e^(((x^(2)+1)/(x)))dx=e^((x^(2)+1)/x)+C and STATEMENT-2 : intf'(x)e^(f(x))dx=e^(f(x))+c

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx