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$\int\sin\left(2u\right)\left(1+\cot\left(2u\right)\right)du$
Learn how to solve integral calculus problems step by step online. Integrate the function sin(2u)(1+cot(2u)). Find the integral. We can solve the integral \int\sin\left(2u\right)\left(1+\cot\left(2u\right)\right)du 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 v), which when substituted makes the integral easier. We see that 2u it's a good candidate for substitution. Let's define a variable v and assign it to the choosen part. Now, in order to rewrite du in terms of dv, we need to find the derivative of v. We need to calculate dv, we can do that by deriving the equation above. Isolate du in the previous equation.