MathProblemsBank

9.2.3 Integrals depending on a parameter

Problem: Prove the formula: \[ I=\int_{0}^{+\infty} x e^{-x^{3}} d x \int_{0}^{+\infty} e^{-x^{3}} d x=\frac{2 \pi \sqrt{3}}{27} \]