An integral involving the squared arctangent of sine squared
Integration by parts followed by differentiation under the integral sign reduces a squared-arctangent trigonometric integral to an elementary antiderivative.
A mathematics notebook
Tagged: feynmans-trick
Notes on integrals, infinite series, and number theory.
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Evaluating a logarithmic Fresnel integral by differentiating under the integral sign
Differentiating the Mellin transform of the sine function with respect to its exponent evaluates a logarithmic Fresnel-type integral in terms of Euler's constant.
Evaluating very nasty logarithmic integrals: Part III
The third part uses complex contours to evaluate logarithmic integrals involving inverse trigonometric functions.