Question Number 149498 by peter frank last updated on 05/Aug/21 $$ \\ $$$$\int\frac{{px}+{q}}{\:\sqrt{{x}^{\mathrm{2}} +{r}^{\mathrm{2}} }} \\ $$ Answered by MJS_new last updated on 05/Aug/21 $$\int\frac{{px}+{q}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 83960 by john santu last updated on 08/Mar/20 $$\int\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$ Commented by mathmax by abdo last updated on 08/Mar/20 $${I}\:=\int\:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −{x}}}{dx}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{2}{x}−\mathrm{1}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 83961 by mathmax by abdo last updated on 08/Mar/20 $${find}\:{I}\:=\int\:{e}^{−{x}} \:{cos}^{\mathrm{4}} {xdx}\:\:{and}\:{J}\:=\int\:{e}^{−{x}} \:{sin}^{\mathrm{4}} \:{xdx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 18396 by Joel577 last updated on 20/Jul/17 $$\int\:\sqrt{\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }}\:\:{dx} \\ $$ Answered by b.e.h.i.8.3.417@gmail.com last updated on 20/Jul/17 $$\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\left({x}^{\mathrm{2}} +{x}\right)^{\mathrm{2}}…
Question Number 83927 by M±th+et£s last updated on 08/Mar/20 $$\int\frac{{sinh}\left({x}\right)+{e}^{\mathrm{3}{x}} }{{sinh}\left({x}\right)−{e}^{{x}} }\:{dx} \\ $$ Answered by TANMAY PANACEA last updated on 08/Mar/20 $$\int\frac{\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{2}}+{e}^{\mathrm{3}{x}}…
Question Number 83923 by jagoll last updated on 08/Mar/20 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{20}}{\left(\mathrm{xsin}\:\mathrm{x}+\mathrm{5cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last updated on 08/Mar/20 $$\Rightarrow\mathrm{xsin}\:\mathrm{x}+\mathrm{5cos}\:\mathrm{x}\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{25}}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{5}}\right)\right)…
Question Number 83921 by jagoll last updated on 08/Mar/20 $$\int\:\:\frac{\mathrm{2x}^{\mathrm{12}} +\mathrm{5x}^{\mathrm{9}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last updated on 08/Mar/20…
Question Number 83917 by turbo msup by abdo last updated on 07/Mar/20 $${find}\:\int\:\:\:\frac{{dx}}{\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} } \\ $$ Answered by redmiiuser last updated on 08/Mar/20 Answered…
Question Number 83898 by sahnaz last updated on 07/Mar/20 $$\int\frac{\mathrm{du}}{\:\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}\:}−\mathrm{u}} \\ $$ Commented by john santu last updated on 07/Mar/20 $$\mathrm{let}\:{u}\:=\:\mathrm{sec}\:\theta\:\Rightarrow\:\mathrm{du}\:=\:\mathrm{sec}\:\theta\:\mathrm{tan}\:\theta\:\mathrm{d}\theta \\ $$ Commented…
Question Number 83899 by john santu last updated on 07/Mar/20 $$\mathrm{Defined}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)=\:\mathrm{nx}\: \\ $$$$\mathrm{for}\:\mathrm{m}\:,\mathrm{n}\:>\:\mathrm{1}\:,\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\int\underset{\mathrm{1}} {\overset{\:\mathrm{m}} {\:}}\left(\mathrm{2n}+\mathrm{6f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right)\right)\:\mathrm{dx}\:\mathrm{is}\:… \\ $$ Commented by john santu…