CalcRef

Integrals · Special Integrals

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.

Worked examples

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

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

Evaluate ∫₀¹ 1/(1+x²) dx.
  1. [arctan x]₀¹ = arctan(1) - arctan(0) = π/4 - 0

Answer: π/4

Related formulas

Integral yielding arcsin

Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.