What is the easiest way to integrateĀ csc^2x/cotx dx

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justaguide eNotes educator| Certified Educator

Here cot x is in the denominator. But it can be seen that the numerator has (csc x)^2. We know that the derivative of cot x is -(csc x)

The integral can be solved in the easiest way by substitution.

Int[ (csc x)^2 / cot x dx]

let y = cot x

-dy = csc x dx

=> Int [ (-1/y) dy]

=> -log|y| + C

substitute y = cot x

=> - log |cot x| + C

The required integral is -log |cot x| + C

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