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Integral yielding arctan

∫1a2+x2 dx=1aarctan⁡(xa)+C\int \frac{1}{a^2 + x^2} \, dx = \frac{1}{a}\arctan\left(\frac{x}{a}\right) + C

An integral that produces the inverse tangent function.

Conditions. a ≠ 0.
  • 2 worked examples
  • 19 in Integrals

Worked examples

Find ∫ 1/(4+x²) dx.
  1. a = 2. (1/2) arctan(x/2) + C

Answer: (1/2) arctan(x/2) + C

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Evaluate ∫₀¹ 1/(1+x²) dx.

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Related formulas

Integral yielding arcsin

See all 19 Integrals formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Integral yielding arctan?

An integral that produces the inverse tangent function. It is one of the integrals formulas in the CalcRef reference.

When does the Integral yielding arctan apply?

The Integral yielding arctan holds under this condition: a ≠ 0.

How do you use the Integral yielding arctan?

Worked example. Find ∫ 1/(4+x²) dx. a = 2. (1/2) arctan(x/2) + C. Answer: (1/2) arctan(x/2) + C.

Practice

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