Find the integral $\frac{1}{9}\int\frac{1}{\cos\left(2x\right)}dx$

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$\frac{1}{9}\int\sec\left(2x\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(1/(cos(2x))dx1/9. Simplify \frac{1}{\cos\left(2x\right)} into \sec\left(2x\right) by applying trigonometric identities. We can solve the integral \int\sec\left(2x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.