Question Number 120395 by bramlexs22 last updated on 31/Oct/20 Answered by Olaf last updated on 31/Oct/20 $$ \\ $$$${u}\:=\:\mathrm{9}{x}^{\mathrm{2}} ,\:{du}\:=\:\mathrm{18}{xdx}\:=\:\mathrm{6}{u}^{\mathrm{1}/\mathrm{2}} {dx} \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{2}} ^{\mathrm{4}} \frac{\mathrm{1}}{\left(\frac{{u}}{\mathrm{3}}\right)^{\mathrm{5}/\mathrm{2}}…
Question Number 54856 by Meritguide1234 last updated on 13/Feb/19 Commented by Meritguide1234 last updated on 14/Feb/19 Commented by Meritguide1234 last updated on 14/Feb/19 Answered by…
Question Number 120374 by bramlexs22 last updated on 31/Oct/20 $$\:\:\:\:\int\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}}\:{dx}\: \\ $$ Answered by Lordose last updated on 31/Oct/20 $$\mathrm{I}\:=\:\int\frac{\mathrm{1}}{\mathrm{x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\mathrm{dx}\:+\:\int\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\mathrm{dx} \\ $$$$\mathrm{I}\:=\:−\mathrm{coth}^{−\mathrm{1}}…
Question Number 54826 by rahul 19 last updated on 13/Feb/19 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\left(\mathrm{1}−{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} −\left(\mathrm{1}−{x}^{\mathrm{4}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \right){dx}\:=\:? \\ $$$$\left.\mathrm{2}\right)\:{If}\:{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{4}\:{then}\:{the}\:{value}\:{of} \\ $$$$\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} {f}\left({x}\right){dx}\:+\:\int_{\mathrm{0}} ^{\:\mathrm{4}}…
Question Number 185880 by cortano1 last updated on 29/Jan/23 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}}}{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}=? \\ $$ Commented by MJS_new last updated on 29/Jan/23 $$\mathrm{simply}\:\mathrm{use}\:{t}=\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}} \\ $$…
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Question Number 185873 by test1234 last updated on 29/Jan/23 $$\left(\mathrm{1}\right)\:\int\pi{x}^{\mathrm{2}} +\sqrt{\frac{{xe}^{\pi} }{{x}^{\mathrm{2}} }}{dx}=? \\ $$$$\left(\mathrm{2}\right)\:\int\frac{\mathrm{ln}\:\left({x}\right)+\mathrm{ln}\:\left(\frac{−{z}}{{x}}\right)}{{x}^{{z}} }+{z}^{{x}} {dx}=? \\ $$ Answered by JDamian last updated on…
Question Number 54797 by afachri last updated on 11/Feb/19 $$ \\ $$$$ \\ $$$$\:\:\:\int\:\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\boldsymbol{{x}}\:+\:\sqrt{\:…..}}}}\:\:\boldsymbol{{dx}}\:\:=\:\:\:? \\ $$$$ \\ $$ Answered by Smail last updated on 11/Feb/19…
Question Number 185863 by normans last updated on 29/Jan/23 Commented by MJS_new last updated on 02/Feb/23 $$\mathrm{do}\:\mathrm{you}\:\mathrm{gain}\:\mathrm{satisfaction}\:\mathrm{by}\:\mathrm{posting} \\ $$$$\mathrm{complicated}\:\mathrm{nonsense}? \\ $$ Answered by MJS_new last…
Question Number 185848 by Mingma last updated on 28/Jan/23 Answered by Frix last updated on 28/Jan/23 $$\int\sqrt{\mathrm{e}^{{x}} +\mathrm{2}}{dx}\:\overset{{t}=\sqrt{\mathrm{e}^{{x}} +\mathrm{2}}} {=}\:\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} −\mathrm{2}}{dt}= \\ $$$$=\mathrm{2}\int{dt}+\sqrt{\mathrm{2}}\int\frac{{dt}}{{t}−\sqrt{\mathrm{2}}}−\sqrt{\mathrm{2}}\int\frac{{dt}}{{t}+\sqrt{\mathrm{2}}}= \\…