`int cot^4 x dx`

int cot^(2) x dx = ?

(i) int sin^-1 x dx (ii) int cos^-1 x dx (iii) int cot^-1 x dx

(i) int tan^2 x dx =____ (ii) int cot^2 x dx = ______

int cot dx

int cosec^2 x dx=- cot x

(i) int x sin^-1 x dx (ii) int x cos^-1 x dx (iii) int x tan^-1 x dx (iv) int x cot^-1 x dx

If (cot x+(cot^(2)x)/(2)+(cot^(3)x)/(3)+...+(cot^(99)x)/(99))+ int(1+cot x)(1+cot^(99)x)dx =-lambda[int cot^(2)xdx+int cot^(3)xdx+int cot^(4)xdx+...+int cot^(98)xdx] , then value of lambda is equal to

int_((pi)/(4))^((pi)/(2))e^(x)(log sin x+cot x)dx

(i) int_0^(pi//4) tan x dx (ii) int_(pi//4)^(pi//2) cot x dx