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Proof: Integral csc(x)(centregalilee.com | Calculus | Integrals | Table of | csc x) conversation of csc x = - ln|csc x + cot x| + C. 1. Evidence Strategy: The strategy is not obvious. Multiply and divide through (csc x + cot x); usage Substitution. csc x dx = csc x csc x + cot x csc x + cot x dx collection u = csc x + cot x climate we discover du = (- csc x cot x - csc2 x) dx instead of du = (- csc x cot x - csc2 x) dx, u = csc x + cot x csc x csc x + cot x csc x + cot x dx = - (- csc2 x - csc x cot x) dx csc x + cot x = - du u deal with integral = - ln |u| + C substitute back u=csc x + cot x = - ln |csc x + cot x| + C Q.E.D.