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int cot^(-1)udx...

int cot^(-1)udx

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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