# How do you find the antiderivative of #sinx/(1+cosx)#?

Finding the pattern is the simplest method.

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To find the antiderivative of ( \frac{\sin(x)}{1 + \cos(x)} ), you can use a substitution. Let ( u = 1 + \cos(x) ). Then, ( du = -\sin(x) , dx ). Substituting, the integral becomes ( -\int \frac{1}{u} , du ), which integrates to ( -\ln|u| + C ), where ( C ) is the constant of integration. Finally, substitute ( u ) back in to get ( -\ln|1 + \cos(x)| + C ).

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