Category: Integration

Question Number 139164 by mathlove last updated on 23/Apr/21 Answered by qaz last updated on 25/Apr/21 $$ln(1-{ae}^{ix})$$$$=ln[1-a(\cos x+i\sin x)]$$$$={ln}\left(\sqrt{\left(\mathrm{1}−{a}\mathrm{cos}\:{x}\right)^{\mathrm{2}} +\left({a}\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{e}^{{i}\mathrm{tan}^{−\mathrm{1}} \frac{−{a}\mathrm{sin}\:{x}}{\mathrm{1}−{a}\mathrm{cos}\:{x}}}…

Question Number 8070 by FilupSmith last updated on 29/Sep/16 $$\mathrm{a}\mathrm{line}L\mathrm{intersec}ts(0,0)andthecurve$$$$y=x^{2}atx=t.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{line}?$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{area}\mathrm{between}L\mathrm{and}y\mathrm{from}$$$$x=0\mathrm{to}x=t?$$ Answered by sandy_suhendra last…

Question Number 139092 by mathdanisur last updated on 22/Apr/21 $$\mathrm{\Omega }=\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{xsinh\left(\pi x\right)e^{-x^2}}{1+x^2}dx$$ Answered by mathmax by abdo last updated on…

Question Number 73545 by Rio Michael last updated on 13/Nov/19 $$evaluate\int lnxdx$$ Commented by Tony Lin last updated on 13/Nov/19 $$integrationbypart$$$$\int{f}\:'\left({x}\right){g}\left({x}\right)={f}\left({x}\right){g}\left({x}\right)−\int{f}\left({x}\right){g}\:'\left({x}\right) \…

Question Number 7960 by tawakalitu last updated on 25/Sep/16 $$\int \frac{4-x}{4+x}dx$$ Commented by Yozzia last updated on 25/Sep/16 $$\int \frac{4-x}{4+x}dx=\int (\frac{8}{4+x}-1)dx=8ln(x+4)-x+c$$ Commented by tawakalitu…