Question Number 228030 by TonyCWX last updated on 12/Mar/26 $${I}\:=\:\int\:\frac{\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{1}}\:{dx}\:=\:\int\:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{4}} −{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −{x}+\mathrm{1}\right)}\:{dx} \\ $$$$=\:\int\:\left[\frac{\mathrm{1}}{\mathrm{5}\left({x}+\mathrm{1}\right)}\:−\:\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}}{\mathrm{5}\left({x}^{\mathrm{4}} −{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −{x}+\mathrm{1}\right)}\right]\:{dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{5}}\int\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{dx}\:−\:\frac{\mathrm{1}}{\mathrm{5}}\int\:\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}}{{x}^{\mathrm{4}}…
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Question Number 227871 by Sid978 last updated on 22/Feb/26 Commented by Kassista last updated on 23/Feb/26 $${are}\:{there}\:{infinitely}\:{many}\:{integrals}?\:{only}\:{the}\:{last}\:{one} \\ $$$${has}\:{a}\:{variable}?\:{what}\:{do}\:{you}\:{mean}\:{with}\:{de}\:{dx}\:{as}\:{an}\:{exponent}? \\ $$ Terms of Service Privacy…
Question Number 227682 by Simurdiera last updated on 13/Feb/26 $$\mathrm{Help}\:\mathrm{please} \\ $$$${I}\:=\:\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}\left({x}\:+\:\mathrm{cos}\left({x}\right)\right)\:{dx} \\ $$ Commented by Tawa11 last updated on 13/Feb/26 https://youtu.be/m5eXP5oyDL4?si=iAaqjq-4F6BUkfoy Answered…
Question Number 227271 by Spillover last updated on 11/Jan/26 Answered by Kassista last updated on 11/Jan/26 $$ \\ $$$$\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{5}}\:{dx}\:=\:\int\:\frac{{x}^{\mathrm{2}} +\mathrm{5}−\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{5}}\:{dx}\:=\:\int\:\frac{{x}^{\mathrm{2}} +\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{5}}\:{dx}\:−\int\frac{\mathrm{5}}{{x}^{\mathrm{2}}…
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Question Number 227146 by Spillover last updated on 03/Jan/26 Answered by Kassista last updated on 03/Jan/26 $$ \\ $$$${I}\:=\:\int_{\:−\mathrm{2}} ^{\:\mathrm{2}\:} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{5}^{{x}} }\:{dx}\:\overset{{x}=−{u}} {\Rightarrow}\int_{\:\mathrm{2}} ^{\:−\mathrm{2}}…
Question Number 227128 by Spillover last updated on 01/Jan/26 Answered by som(math1967) last updated on 01/Jan/26 $$\int_{\mathrm{0}\:\:} ^{\frac{\pi}{\mathrm{2}}} \frac{\sqrt{{tanx}}}{\mathrm{1}+\sqrt{{tanx}}}{dx} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\sqrt{{tan}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}{dx}}{\mathrm{1}+\sqrt{{tan}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}} \\ $$$${I}=\int_{\mathrm{0}}…