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Extension: Differentiation Under the Integral Sign

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Explanations 1

The technique of differentiation under the integral sign, popularly known as Feynman's trick, is a way to impress your friends and colleagues in dire circumstances: Often, integ…
By Victor Wang

Problems 2

Let I=∫0∞e−xsin⁡xxdxI = \int_0^{\infty} \frac{e^{-x}\sin{x}}{x} dxI=∫0∞xe−xsinxdx. Find π/I\pi/Iπ/I. Source: HMMT February 2007
(ASMT 2015 Calculus Tiebreaker #1) Compute: ∫01x29ln⁡xdx.\int_{0}^{1}x^{29}\ln x dx.∫01x29lnxdx.