calculate-0-ln-x-1-x-3-dx- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 79096 by mathmax by abdo last updated on 22/Jan/20 calculate∫0∞ln(x)(1+x)3dx Commented by mind is power last updated on 22/Jan/20 samideewillworckfor∫0+∞ln(x)p(x+1)rdxwither>1,p∈Nln(x)p=∂p∂tpxt∣t=0andsamidealikepreviousonebutwewillhavemorcomplicatedfunctionΨp(x)…. Answered by mind is power last updated on 22/Jan/20 ln(x)=ddxxt∣t=0f(t)=∫0+∞xt(1+x)3dx,wewantf′(0)x=tg2(y)⇒f(t)=∫0π2tg2t(y)(1+tg2(y))3.2(1+tg2(y))tg(y)dy=2∫0π2tg2t+1(y)(1+tg2(y))2dy=2∫0π2sin2t+1(y)cos−2t+3(y)dy=β(t+1,−t+2)=Γ(t+1)Γ(2−t)Γ(3)=Γ(t+1)Γ(2−t)2f(t)=Γ(t+1)Γ(2−t)2f′(t)=12{Γ′(t+1)Γ(2−t)−Γ′(2−t)Γ(t+1)}=12{Ψ(t+1)Γ(t+1)Γ(2−t)−Ψ(2−t)Γ(2−t)Γ(t+1)}f′(0)=12{Ψ(1)−Ψ(2)}=12{−γ−(1−γ)}=−12=−0.5 Commented by msup trace by abdo last updated on 23/Jan/20 thankyousirnowtrytosolveitcomplexanalysis… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-n-2-1-n-4-1-Next Next post: calculate-n-2-1-n-n-4-1- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.