Find the integral of $\frac{1}{\sec\left(2x\right)+\tan\left(2x\right)}\left(2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2\right)$

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$\int\frac{1}{\sec\left(2x\right)+\tan\left(2x\right)}\left(2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2\right)dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral of 1/(sec(2x)+tan(2x))(2sec(2x)tan(2x)+2sec(2x)^2). Find the integral. Multiplying the fraction by 2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2. Rewrite the trigonometric expression \frac{2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2}{\sec\left(2x\right)+\tan\left(2x\right)} inside the integral. The integral of a function times a constant (2) is equal to the constant times the integral of the function.