Final Answer
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Expand the fraction $\frac{2\cot\left(x\right)-3\sin\left(x\right)}{\sin\left(x\right)}$ into $2$ simpler fractions with common denominator $\sin\left(x\right)$
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$\int\left(\frac{2\cot\left(x\right)}{\sin\left(x\right)}+\frac{-3\sin\left(x\right)}{\sin\left(x\right)}\right)dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int((2cot(x)-3sin(x))/sin(x))dx. Expand the fraction \frac{2\cot\left(x\right)-3\sin\left(x\right)}{\sin\left(x\right)} into 2 simpler fractions with common denominator \sin\left(x\right). Simplify the resulting fractions. Simplify the expression inside the integral. We can solve the integral \int\frac{\cos\left(x\right)}{\sin\left(x\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(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.