An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u = tan (x/2) or equivalently x = 2 tan^-1 u. The following relations are used in making this change of variables.

Evaluate

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и 2 du B: sin xх %— 2u |A: dx = C: cos x = 1+ и? 1+ и? 1 + и? dx 1 - cos x