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Question Number 124920 by mathmax by abdo last updated on 07/Dec/20
calculate∫0∞e−xndx
Answered by Dwaipayan Shikari last updated on 07/Dec/20
∫0∞e−xndxxn=u⇒nxn−1=dudx⇒1n∫0∞x1−ne−udu=1n∫0∞u1−nne−udu=1nΓ(1n)=Γ(n+1n)
Answered by mathmax by abdo last updated on 07/Dec/20
An=∫0∞e−xndxwedothechangementx=t1n⇒An=∫0∞e−t×1nt1n−1dt=1n∫0∞t1n−1e−tdt=1n×Γ(1n)
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