Question Number 69110 by Fawole last updated on 20/Sep/19 $${Evaluate}\:\int_{−\infty} ^{\infty} \frac{{cos}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Sep/19 $$\:\:{let}\:{I}\:=\int_{−\infty}…
Question Number 134641 by benjo_mathlover last updated on 06/Mar/21 $$\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} \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\mathrm{1}}{\mathrm{1}+{sinu}}{du}−{x}\:\: \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\int\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 134636 by bobhans last updated on 06/Mar/21 $$\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…
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:…
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 $$\sqrt{\frac{\mathrm{x}\sqrt{\mathrm{x}}+\mathrm{4}}{\:\sqrt{\mathrm{x}}}}\:=\:\frac{\sqrt{\mathrm{x}\sqrt{\mathrm{x}}+\mathrm{4}}}{\:\sqrt[{\mathrm{4}}]{\mathrm{x}}}\: \\ $$$$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{t}^{\mathrm{4}} \:\Rightarrow\mathrm{dx}\:=\:\mathrm{4t}^{\mathrm{3}} \:\mathrm{dt} \\…
Question Number 134591 by bobhans last updated on 05/Mar/21 $$\mathrm{Precalculus} \\ $$What is the volume of the solid obtained by rotating the region bounded by…
Question Number 134587 by bobhans last updated on 05/Mar/21 $$\mathrm{Precalculus}\: \\ $$How do I find the volume of a solid obtained by rotating the region…
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Question Number 134580 by metamorfose last updated on 05/Mar/21 $$\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…
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…