a golden integral @drpeyam

Uploaded October 2024 | Updated September 2026, 1 week ago

a golden trig integral

We calculate the integral of sin(x)+cos(x)/sin^5(x)+cos^5(x) from 0 to pi/2 using first a u-substitution (or u-sub) followed by a trigonometric substitution, and the Gamma function or Euler's identity. The result involves square roots and the golden ratio, which was used in the Renaissance as a standard of beauty. This is a must-see for any calculus lover or any lover of gold and beauty, enjoy!

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