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- Weierstrass Substitution
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Apply the formula: $\int\csc\left(\theta \right)^n\cos\left(\theta \right)dx$$=\int\frac{\cos\left(\theta \right)}{\sin\left(\theta \right)^n}dx$, where $x=3x$ and $n=2$
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$\int\frac{\cos\left(3x\right)}{\sin\left(3x\right)^2}dx$
Learn how to solve problems step by step online. int(csc(3x)^2cos(3x))dx. Apply the formula: \int\csc\left(\theta \right)^n\cos\left(\theta \right)dx=\int\frac{\cos\left(\theta \right)}{\sin\left(\theta \right)^n}dx, where x=3x and n=2. We can solve the integral \int\frac{\cos\left(3x\right)}{\sin\left(3x\right)^2}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 \sin\left(3x\right) 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.
