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Expand the fraction $\frac{\sin\left(x\right)+\cos\left(x\right)}{\sin\left(2x\right)}$ into $2$ simpler fractions with common denominator $\sin\left(2x\right)$
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$\int\left(\frac{\sin\left(x\right)}{\sin\left(2x\right)}+\frac{\cos\left(x\right)}{\sin\left(2x\right)}\right)dx$
Learn how to solve integrals of rational functions problems step by step online. Solve the trigonometric integral int((sin(x)+cos(x))/sin(2x))dx. Expand the fraction \frac{\sin\left(x\right)+\cos\left(x\right)}{\sin\left(2x\right)} into 2 simpler fractions with common denominator \sin\left(2x\right). Simplify the expression inside the integral. The integral \int\frac{1}{2\cos\left(x\right)}dx results in: \frac{1}{2}\ln\left(\sec\left(x\right)+\tan\left(x\right)\right). The integral \int\frac{1}{2\sin\left(x\right)}dx results in: -\frac{1}{2}\ln\left(\csc\left(x\right)+\cot\left(x\right)\right).