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Category: Integration

Question-170725

Question Number 170725 by Sotoberry last updated on 29/May/22 Answered by FelipeLz last updated on 30/May/22 $${u}\:=\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\Rightarrow\:{du}\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$${dv}\:=\:\mathrm{1}{dx}\:\Rightarrow\:{v}\:=\:{x} \\ $$$$\int\mathrm{tan}^{−\mathrm{1}} \left({x}\right){dx} \\…

Question-170663

Question Number 170663 by kndramaths last updated on 28/May/22 Commented by kaivan.ahmadi last updated on 28/May/22 $${a}. \\ $$$$\mathrm{0}\leqslant{x}\leqslant{a}\:\:,\:\:\mathrm{0}\leqslant{y}\leqslant\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} } \\ $$$$\int\frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{1}}{{a}}{arctg}\left(\frac{{x}}{{a}}\right)…

Question-170593

Question Number 170593 by 119065 last updated on 27/May/22 Commented by mkam last updated on 27/May/22 $$\int\:\left({x}+\mathrm{3}\:−\:\mathrm{3}\right)\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx}=\int\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{3}\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$ \\ $$$$=\:\frac{\mathrm{2}}{\mathrm{5}}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:−\:\mathrm{2}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…