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Category: Integration

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

Question Number 7506 by gourav~ last updated on 01/Sep/16 $$\int\left\{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}\right\}^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{dx}}{{x}}=? \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzia last updated on 01/Sep/16 $${Let}\:{I}=\int\frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}{dx}.…

Question-73037

Question Number 73037 by aliesam last updated on 05/Nov/19 Commented by mathmax by abdo last updated on 06/Nov/19 $$\left.\mathrm{1}\right)\:{I}_{\mathrm{0}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{\mathrm{1}−{x}} {dx}\:=\left[−{e}^{\mathrm{1}−{x}} \right]_{\mathrm{0}} ^{\mathrm{1}}…

1-x-2-3-1-x-dx-

Question Number 7482 by kishanjith last updated on 31/Aug/16 $$\int\frac{\left(\mathrm{1}+{x}\right)^{−\mathrm{2}/\mathrm{3}} }{\left(\mathrm{1}+{x}\right)}{dx} \\ $$ Answered by sandy_suhendra last updated on 31/Aug/16 $$=\int\left(\mathrm{1}−{x}\right)^{\frac{−\mathrm{5}}{\mathrm{3}}} {dx} \\ $$$${let}\:\:\:{U}=\mathrm{1}−{x}\: \\…

tanx-dx-

Question Number 73012 by vishalbhardwaj last updated on 05/Nov/19 $$\int\sqrt{{tan}\mathrm{x}}\:{d}\mathrm{x} \\ $$ Answered by mind is power last updated on 05/Nov/19 $$\mathrm{u}=\sqrt{\mathrm{tan}\left(\mathrm{x}\right)} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{arctan}\left(\mathrm{u}^{\mathrm{2}} \right)\Rightarrow\mathrm{dx}=\frac{\mathrm{2u}}{\mathrm{1}+\mathrm{u}^{\mathrm{4}}…