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Which of the Following Methods Is Most Efficient for Evaluating the Integral: Int Cot4(x)csc^2(x)dx Select Only ONE Answer

Question

Which of the following methods is most efficient for evaluating the integral: int cot4(x)csc^2(x)dx Select only ONE answer straight-forward u-substitution using trig integration (with the identity csc^2(x)=cot^2(x)-1) Ore-write everything in terms of sine and cosine using trig integration (by first splitting up the integrand as cot^3(x)csc(x)cot(x)csc(x) , and then using the appropriate trig identity

Solution

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Answer

### straight-forward u-substitution

Explanation

## Step 1: Analyze the integral### The integral involves and . The derivative of is . This suggests a u-substitution with .## Step 2: Perform u-substitution### Let . Then . The integral becomes .## Step 3: Evaluate the integral### .## Step 4: Substitute back### Substituting back , we get .