Menu Close

Category: Integration

B-1-sin-6x-1-sin-6x-dx-

Question Number 134641 by benjo_mathlover last updated on 06/Mar/21 $$\mathscr{B}\:=\:\int\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{6}{x}}{\mathrm{1}+\mathrm{sin}\:\mathrm{6}{x}}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 06/Mar/21 $$\int\frac{\mathrm{2}}{\mathrm{1}+{sin}\mathrm{6}{x}}−\mathrm{1}{dx}\:\:\:\:\:\:\:\mathrm{6}{x}={u} \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\mathrm{1}}{\mathrm{1}+{sinu}}{du}−{x}\:\: \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\int\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…

INTEGRAL-1-0-ln-2-x-2-e-1-x-dx-2-sin-x-cos-x-sin-4-x-cos-4-x-dx-

Question Number 134636 by bobhans last updated on 06/Mar/21 $$\mathcal{INTEGRAL} \\ $$$$\left(\mathrm{1}\right)\int_{\mathrm{0}} ^{\:\mathrm{ln}\:\mathrm{2}} \:{x}^{−\mathrm{2}} .{e}^{−\frac{\mathrm{1}}{{x}}} \:{dx}\:=? \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by benjo_mathlover…

n-1-1-n-1-H-n-n-2-

Question Number 134619 by payamnazerian last updated on 05/Mar/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} \boldsymbol{{H}}_{{n}} }{\boldsymbol{{n}}^{\mathrm{2}} }=??? \\ $$ Terms of Service Privacy Policy Contact:…

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…