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Category: Integration

solve-x-Inx-dx-

Question Number 185959 by Michaelfaraday last updated on 30/Jan/23 $${solve}: \\ $$$$\int{x}^{{Inx}} {dx} \\ $$ Answered by Frix last updated on 30/Jan/23 $$\int{x}^{\mathrm{ln}\:{x}} {dx}\:\overset{{t}=\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{ln}\:{x}} {=}\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{e}}}\int\mathrm{e}^{{t}^{\mathrm{2}}…

Question-185944

Question Number 185944 by Michaelfaraday last updated on 30/Jan/23 Commented by mr W last updated on 30/Jan/23 $${this}\:{app}\:{is}\:{developed}\:{for}\:{writting} \\ $$$${mathematical}\:{formulas}.\:{is}\:{it}\:{not} \\ $$$${easier}\:{and}\:{better}\:{for}\:{you}\:{to}\:{write} \\ $$$$\int{x}^{\mathrm{3}} \:\mathrm{ln}\:\left({x}+\mathrm{4}\right)\:{dx}\:{instead}\:{of}\:…

1-cos-x-1-cos-x-cos-x-dx-

Question Number 185935 by cortano1 last updated on 30/Jan/23 $$\:\:\:\int\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)\:\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 30/Jan/23 $${I}=\int\frac{\mathrm{1}−\mathrm{cos}{x}}{\left(\mathrm{1}+\mathrm{cos}{x}\right)\mathrm{cos}{x}}{dx}=\int\frac{\left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{2}} }{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\right)\mathrm{cos}{x}}{dx} \\ $$$$\:\:=\int\frac{\mathrm{1}−\mathrm{2cos}{x}+\mathrm{cos}^{\mathrm{2}}…

Question-120395

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}}…

1-x-2-x-dx-

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}}…

1-0-1-1-x-7-1-4-1-x-4-1-7-dx-2-If-f-x-x-3-3x-4-then-the-value-of-1-1-f-x-dx-0-4-f-1-x-dx-3-pi-pi-1-cosx-cos2x-cos13x-1-sinx-si

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}}…

0-pi-2-tan-x-1-3-sin-x-cos-x-2-dx-

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 $$\mathrm{simply}\:\mathrm{use}\:{t}=\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}} \\ $$…