Menu Close

Category: Integration

x-2-1-x-1-2x-dx-

Question Number 88131 by M±th+et£s last updated on 08/Apr/20 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx} \\ $$ Answered by MJS last updated on 08/Apr/20 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{1}−\mathrm{2}{x}}\:\rightarrow\:{dx}−\sqrt{\mathrm{1}−\mathrm{2}{x}}{dt}\right] \\…

dx-x-1-x-

Question Number 88118 by sahnaz last updated on 08/Apr/20 $$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)×\sqrt{\mathrm{x}}} \\ $$ Commented by mathmax by abdo last updated on 08/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}}}\:\Rightarrow{I}\:=_{{x}={t}^{\mathrm{2}} } \:\:\int\:\:\:\frac{\mathrm{2}{tdt}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right){t}}\:=\mathrm{2}\:\int\:\:\frac{{dt}}{{t}^{\mathrm{2}}…

dx-2x-3-2-3-

Question Number 88097 by sahnaz last updated on 08/Apr/20 $$\int\frac{\mathrm{dx}}{\left(\mathrm{2x}−\mathrm{3}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$ Answered by john santu last updated on 08/Apr/20 $$\int\:{t}^{−\mathrm{2}/\mathrm{3}} ×\frac{\mathrm{1}}{\mathrm{2}}{dt}\:\:\:\left[\:{t}\:=\:\mathrm{2}{x}−\mathrm{3}\:\right] \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{3}\:×\:\sqrt[{\mathrm{3}\:\:}]{{t}}\:+\:{c}\:…

Question-88069

Question Number 88069 by Power last updated on 08/Apr/20 Commented by Power last updated on 08/Apr/20 $$\lfloor\mathrm{x}\rfloor−\mathrm{greatest}\:\mathrm{integer}\: \\ $$$$\mathrm{x}=\lfloor\mathrm{x}\rfloor+\left\{\mathrm{x}\right\}\:\:\:\:\:\:\:\mathrm{0}\leqslant\left\{\mathrm{x}\right\}<\mathrm{1} \\ $$ Commented by mathmax by…

dx-cos-x-2-sin-x-

Question Number 88064 by jagoll last updated on 08/Apr/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}\left(\mathrm{2}+\mathrm{sin}\:\mathrm{x}\right)}? \\ $$ Answered by john santu last updated on 08/Apr/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{2}+\mathrm{sin}\:\mathrm{x}\right)}\:=\:\int\frac{\mathrm{d}\left(\mathrm{sin}\:\mathrm{x}\right)}{\left(\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)\left(\mathrm{2}+\mathrm{sin}\:\mathrm{x}\right)} \\ $$$$\left[\:\mathrm{let}\:\mathrm{2}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{t}\:\right]…