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MathCalculus

Inverse Trig Integrals: Find ∫dx/(25 + 4x²)

Use a scaling substitution to evaluate OpenStax Checkpoint 1.42 and confirm the inverse tangent coefficient by differentiation.

Question

OpenStax Calculus Volume 2, §1.7, Checkpoint 1.42: Use substitution to find the antiderivative

∫dx25+4x2.\int\frac{dx}{25+4x^2}.

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Evidence boundary

The checkpoint asks for an antiderivative and supplies no initial value. The result applies for all real xx and contains an arbitrary constant.