" 13."quad cot^(2)xdx=

int cot^(2)xdx

int cot^2xdx=

int cot^(7)xdx=

int7x cot^(2)xdx

int cot^(-1)xdx

int cot^(4) xdx

int cot^(5) xdx

int cot xdx

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/3)cot^(2)xdx=?