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Category: Integration

3-x-4-x-dx-

Question Number 134601 by abdullahquwatan last updated on 05/Mar/21 $$\int\mathrm{3}\left(\sqrt{\mathrm{x}\:+\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{x}}}}\right)\:\mathrm{dx} \\ $$ Answered by bobhans last updated on 06/Mar/21 $$\sqrt{\frac{\mathrm{x}\sqrt{\mathrm{x}}+\mathrm{4}}{\:\sqrt{\mathrm{x}}}}\:=\:\frac{\sqrt{\mathrm{x}\sqrt{\mathrm{x}}+\mathrm{4}}}{\:\sqrt[{\mathrm{4}}]{\mathrm{x}}}\: \\ $$$$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{t}^{\mathrm{4}} \:\Rightarrow\mathrm{dx}\:=\:\mathrm{4t}^{\mathrm{3}} \:\mathrm{dt} \\…

tan-x-dx-

Question Number 134580 by metamorfose last updated on 05/Mar/21 $$\int\sqrt{{tan}\left({x}\right)}{dx}=…? \\ $$ Answered by Olaf last updated on 05/Mar/21 $$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{arccos}\left(\mathrm{cos}{x}−\mathrm{sin}{x}\right) \\ $$$$+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\mathrm{cos}{x}+\mathrm{sin}{x}+\sqrt{\mathrm{sin2}{x}}\right)+\mathrm{C} \\ $$ Answered…

1-let-f-a-a-tanx-dx-with-a-gt-0-find-a-explicit-form-for-f-x-2-find-also-g-a-dx-a-tanx-3-calculate-2-tanx-dx-and-dx-2-tanx-

Question Number 69044 by mathmax by abdo last updated on 18/Sep/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({a}\right)\:=\int\sqrt{{a}+{tanx}}{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({a}\right)\:=\int\:\:\frac{{dx}}{\:\sqrt{{a}+{tanx}}} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int\sqrt{\mathrm{2}+{tanx}}{dx}\:{and}\:\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}+{tanx}}} \\ $$ Answered by mind is power…

R-0-3a-x-3a-x-x-a-dx-

Question Number 134547 by EDWIN88 last updated on 05/Mar/21 $$\mathscr{R}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}{a}} {x}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:{dx}\: \\ $$ Answered by liberty last updated on 05/Mar/21 $$\mathrm{by}\:\mathrm{change}\:\mathrm{of}\:\mathrm{variable}\: \\ $$$$\:\mathrm{let}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:={h}\:\Rightarrow\:{x}=\frac{−{ah}^{\mathrm{2}} +\mathrm{3}{a}}{{h}^{\mathrm{2}}…