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$\int\left(\frac{1+\sin\left(x\right)}{\cos\left(x\right)}+\frac{\cos\left(x\right)}{1-\sin\left(x\right)}\right)dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (1+sin(x))/cos(x)+cos(x)/(1-sin(x)). Find the integral. Expand the integral \int\left(\frac{1+\sin\left(x\right)}{\cos\left(x\right)}+\frac{\cos\left(x\right)}{1-\sin\left(x\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1+\sin\left(x\right)}{\cos\left(x\right)}dx results in: \ln\left(\sec\left(x\right)+\tan\left(x\right)\right)-\ln\left(\cos\left(x\right)\right). Gather the results of all integrals.