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Integrals · Basic Antiderivatives

Integral of csc²(x)

∫csc⁡2x dx=−cot⁡x+C\int \csc^2 x \, dx = -\cot x + C

The antiderivative of cosecant squared is negative cotangent.

  • 2 worked examples
  • 19 in Integrals

Worked examples

Find ∫ csc²(3x) dx.
  1. Let u = 3x, du = 3dx. (1/3)∫ csc²u du = -(1/3)cot u + C

Answer: -(1/3)cot(3x) + C

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Evaluate ∫_(π/4)^(π/2) csc²x dx.

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Common questions

What is the Integral of csc²(x)?

The antiderivative of cosecant squared is negative cotangent. It is one of the integrals formulas in the CalcRef reference.

How do you use the Integral of csc²(x)?

Worked example. Find ∫ csc²(3x) dx. Let u = 3x, du = 3dx. (1/3)∫ csc²u du = -(1/3)cot u + C. Answer: -(1/3)cot(3x) + C.

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