`int (x dx)/(1-xcotx)=`

Evaluate the following integrals: (i) int 2x sqrt(1 + x^2)dx " " (ii) int e^(-x^2) x dx " " (iii) int (sin x)/(1 + cos x) dx (iv) int 1/(1 + x^2)dx " " (v) int x (a - x)^8 dx .

int dx/(x+1)

int(x)/(x+1)dx

int 1/(1-x) dx

(i) int(1)/((1+cos2x))dx , (ii) int (1)/((1-cos2x)) dx

lim_(x rarr0)(xcotx)

int|x|*1dx

int(dx)/(x(x+1))=

inte^x(1-cotx+cot^2x)dx= e^xcotx+C (b) e^xcotx+C (c) e^x\ cos e c\ x+C (d) e^x\ cos e c\ x+C

int (dx)/((x+1)(2x+1)) (ii) int (x-1)/((x-2)(x-3)) dx .