`int cot^(5)xdx=A*cot^(4)x+B*cot^(2)x+log[f(x)]+c` ,then `[A,B,f(x)]=`

int7x cot^(2)xdx

int cot^(5)xdx cot xdx

int cot^(4)xdx cot xdx

int(cot^(2)x+cot^(4)x)dx=

int cot^(3)x cos ec^(4)xdx

int sin x cot^(3)xdx

int cot^6x cosec^2xdx

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

x^(2)cot^(-1)xdx