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Category: Integration

1-show-that-1-1-dx-x-2-2x-2-ln-5-2-2-determine-1-dx-x-1-x-3-test-the-convergence-of-the-series-given-by-r-1-r-1-r-e-r-4-obtain-3-non-zero-te

Question Number 174421 by ali009 last updated on 31/Jul/22 $$\left.\mathrm{1}\right)\:{show}\:{that} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{−{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}}={ln}\left(\sqrt{\mathrm{5}}−\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right) \\ $$$${determine} \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}}} \\ $$$$\left.\mathrm{3}\right)\:{test}\:{the}\:{convergence}\:{of}\:{the}\:{series}\:{given}\:{by}…

determine-whether-the-following-integral-are-convergence-or-divergence-1-1-3-4-2x-dx-2-1-2-x-2-8-x-3-dx-

Question Number 174420 by ali009 last updated on 31/Jul/22 $${determine}\:{whether}\:{the}\:{following}\:{integral} \\ $$$${are}\:{convergence}\:{or}\:{divergence} \\ $$$$\left.\mathrm{1}\right)\int_{−\infty} ^{\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}−\mathrm{2}{x}}{dx} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{8}−{x}^{\mathrm{3}} }}{dx} \\ $$ Answered…

using-the-substitution-u-x-2-evaluate-1-2-x-1-x-2-4-

Question Number 43342 by pieroo last updated on 10/Sep/18 $$\mathrm{using}\:\mathrm{the}\:\mathrm{substitution}\:\mathrm{u}=\mathrm{x}+\mathrm{2},\:\mathrm{evaluate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$ Answered by $@ty@m last updated on 10/Sep/18 $$\underset{\mathrm{3}} {\overset{\mathrm{4}} {\int}}\frac{\left({u}−\mathrm{2}\right)−\mathrm{1}}{{u}^{\mathrm{4}}…

let-f-x-0-x-t-1-sint-dt-1-find-a-explicit-form-of-f-x-2-calculate-0-t-1-sint-dt-

Question Number 43337 by math khazana by abdo last updated on 09/Sep/18 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\frac{{t}}{\mathrm{1}+{sint}}{dt} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}}{\mathrm{1}+{sint}}\:{dt}\: \\ $$ Commented by…

Question-43324

Question Number 43324 by Raj Singh last updated on 09/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 09/Sep/18 $$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{x}^{\mathrm{2}} +\mathrm{1}+{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}}…

Question-43322

Question Number 43322 by Raj Singh last updated on 09/Sep/18 Commented by maxmathsup by imad last updated on 11/Sep/18 $${let}\:{A}\:=\:\int\:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)}\:{let}\:{decompose}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)} \\…

Question-43319

Question Number 43319 by Meritguide1234 last updated on 09/Sep/18 Answered by MJS last updated on 09/Sep/18 $$\frac{\mathrm{8}{x}+\frac{\mathrm{8}}{{x}}+\mathrm{9}}{\left(\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}\right)^{\mathrm{2}} }=\frac{\mathrm{8}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{8}}{{x}\left(\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}\right)^{\mathrm{2}} }= \\…

Question-108841

Question Number 108841 by 150505R last updated on 19/Aug/20 Answered by mathmax by abdo last updated on 19/Aug/20 $$\mathrm{let}\:\mathrm{take}\:\mathrm{a}\:\mathrm{try}\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{asinx}\:+\mathrm{bcosx}\right)\mathrm{dx}\:\Rightarrow \\ $$$$\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{asinx}\right)\mathrm{dx}+\int_{\mathrm{0}}…