Question Number 4071 by Yozzii last updated on 27/Dec/15 Commented by Yozzii last updated on 27/Dec/15 $${Just}\:{sharing}\:{some}\:{problems}\:{I}\:{did} \\ $$$${today}. \\ $$ Terms of Service Privacy…
Question Number 69597 by ozodbek last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${generally}\:{let}\:{find}\:{f}\left({a}\right)\:=\int\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${changement}\:{x}\:={ash}\left({t}\right)\:{give}\:{f}\left({a}\right)=\int{ach}\left({t}\right){ach}\left({t}\right){dt} \\ $$$$={a}^{\mathrm{2}}…
Question Number 69603 by Mikael last updated on 25/Sep/19 $$\int\:{x}^{\mathrm{3}} {arcsinxdx} \\ $$ Answered by MJS last updated on 25/Sep/19 $$\mathrm{by}\:\mathrm{parts} \\ $$$$\int{u}'{v}={uv}−\int{uv}' \\ $$$${u}'={x}^{\mathrm{3}}…
Question Number 69573 by Ajao yinka last updated on 25/Sep/19 Commented by mind is power last updated on 25/Sep/19 $${i}\:{will}\:{try}\:{later}\:{now}\:{nothing}\:{goes}\:{wellfor}\:{this}\:{one} \\ $$ Terms of Service…
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Question Number 69566 by Ajao yinka last updated on 25/Sep/19 Answered by mind is power last updated on 25/Sep/19 $$=\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\sum_{{k}=\mathrm{0}} ^{{x}} \int_{{k}} ^{{k}+\mathrm{1}} \left({x}−{k}\right)^{{k}}…
Question Number 135103 by frc2crc last updated on 10/Mar/21 $${f}\left({x}\right)=\mathrm{1}+\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{{n}} \\ $$ Commented by Dwaipayan Shikari last updated on 10/Mar/21 $$\mathrm{1}−\left(−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}}…
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Question Number 69564 by mathmax by abdo last updated on 25/Sep/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+{a}}\:\:\:{with}\:{a}\:{real}\:{and}\:{a}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…
Question Number 69563 by mathmax by abdo last updated on 25/Sep/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated…