Question Number 55995 by maxmathsup by imad last updated on 07/Mar/19 $${find}\:{I}\:=\int\:\:{arctan}\left(\mathrm{1}−{x}\right){dx}\:\:{and}\:{J}\:=\int\:{actan}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 08/Mar/19 $${by}\:{psrts}\:{I}\:={x}\:{arctan}\left(\mathrm{1}−{x}\right)−\int\:{x}\:\frac{−\mathrm{1}}{\mathrm{1}+\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }{dx}…
Question Number 55994 by maxmathsup by imad last updated on 07/Mar/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({x}^{\mathrm{2}} −{x}\right){dx} \\ $$ Answered by MJS last updated on 08/Mar/19 $$\int\mathrm{arctan}\:\left({x}^{\mathrm{2}}…
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Question Number 121519 by benjo_mathlover last updated on 09/Nov/20 $$\:\:\int\:\frac{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 09/Nov/20 $$\:\int\:\frac{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{3}}…
Question Number 187050 by normans last updated on 13/Feb/23 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\:\frac{\boldsymbol{{cos}}^{−\mathrm{1}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}{\boldsymbol{{Ln}}\:\boldsymbol{{x}}}\:\:\boldsymbol{{dx}}\:=??\:\:\: \\ $$$$ \\ $$ Commented by Frix last updated on…
Question Number 121498 by Lordose last updated on 08/Nov/20 $$ \\ $$$$\mathrm{Evaluate} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}\right)}{\mathrm{n}} \\ $$ Answered by Bird last updated on 09/Nov/20…
Question Number 121500 by bramlexs22 last updated on 08/Nov/20 $$\:\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{2}} +\mathrm{9}}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)−\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)=\:\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{5}}\right) \\ $$ Commented by benjo_mathlover last updated on 08/Nov/20 $$\mathrm{i}\:\mathrm{think}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\: \\…
Question Number 121492 by mathmax by abdo last updated on 08/Nov/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Answered by mnjuly1970 last updated on 09/Nov/20…
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Question Number 121466 by sdfg last updated on 08/Nov/20 $$\int\sqrt{{cos}\left({x}\right)\:{dx}} \\ $$ Commented by MJS_new last updated on 08/Nov/20 $$\int\sqrt{\mathrm{cos}\:{x}\:{dx}}\:\mathrm{or}\:\int\sqrt{\mathrm{cos}\:{x}}\:{dx}? \\ $$ Commented by sdfg…