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$\int\left(\frac{\sin\left(x\right)}{1-\cos\left(x\right)}+\frac{-\sin\left(x\right)\cos\left(x\right)}{1+\cos\left(x\right)}\right)dx$
Learn how to solve integral calculus problems step by step online. Integrate the function sin(x)/(1-cos(x))+(-sin(x)cos(x))/(1+cos(x)). Find the integral. Simplify the expression inside the integral. The integral \int\frac{\sin\left(x\right)}{1-\cos\left(x\right)}dx results in: \ln\left(1-\cos\left(x\right)\right). The integral -\int\frac{\sin\left(2x\right)}{2\left(1+\cos\left(x\right)\right)}dx results in: 1+\cos\left(x\right)-\ln\left(1+\cos\left(x\right)\right).