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** Step-by-step Solution **

** How should I solve this problem?

- Integrate using basic integrals
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Product of Binomials with Common Term
- FOIL Method
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The integral of a function times a constant ($6$) is equal to the constant times the integral of the function

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$6\int\csc\left(5x\right)\cot\left(5x\right)dx$

Learn how to solve problems step by step online. Solve the trigonometric integral int(6csc(5x)cot(5x))dx. The integral of a function times a constant (6) is equal to the constant times the integral of the function. We can solve the integral \int\csc\left(5x\right)\cot\left(5x\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 5x 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.

** Final answer to the problem

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