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Category: Integration

dx-1-x-2-x-n-n-1-1-2-z-n-1-n-1-z-n-1-n-1-cccccc-where-z-

Question Number 22621 by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{x}\right)^{\mathrm{n}} }\left(\mathrm{n}\neq\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{z}^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{z}^{\mathrm{n}−\mathrm{1}} }{\mathrm{n}−\mathrm{1}}\right)+\mathrm{cccccc} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\mathrm{z}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…

How-is-x-sin-x-1-cos-x-dx-xtan-x-2-C-

Question Number 22623 by tawa tawa last updated on 21/Oct/17 $$\mathrm{How}\:\mathrm{is}:\:\:\:\int\:\frac{\mathrm{x}\:+\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\mathrm{xtan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:+\:\mathrm{C} \\ $$ Answered by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{x}+\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}\mathrm{dx}\:\: \\ $$$$\int\frac{\mathrm{x}}{\mathrm{2cos}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}+\frac{\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}}…

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}\:…