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 Number 43324 by Raj Singh last updated on 09/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 09/Sep/18 $$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{x}^{\mathrm{2}} +\mathrm{1}+{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}}…
Question Number 43322 by Raj Singh last updated on 09/Sep/18 Commented by maxmathsup by imad last updated on 11/Sep/18 $${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 Number 43319 by Meritguide1234 last updated on 09/Sep/18 Answered by MJS last updated on 09/Sep/18 $$\frac{\mathrm{8}{x}+\frac{\mathrm{8}}{{x}}+\mathrm{9}}{\left(\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}\right)^{\mathrm{2}} }=\frac{\mathrm{8}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{8}}{{x}\left(\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}\right)^{\mathrm{2}} }= \\…
Question Number 108841 by 150505R last updated on 19/Aug/20 Answered by mathmax by abdo last updated on 19/Aug/20 $$\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 \\ $$$$\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{asinx}\right)\mathrm{dx}+\int_{\mathrm{0}}…
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Question Number 108839 by 150505R last updated on 19/Aug/20 Commented by Her_Majesty last updated on 20/Aug/20 $${this}\:{looks}\:{to}\:{me}\:{as}\:{if}\:{the}\:{integral}\:{must}\:{be} \\ $$$$\frac{{p}\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }{{x}^{{q}} }\:{with}\:{p},\:{q}\:\in\mathbb{Q} \\ $$$$\frac{{d}}{{dx}}\left[\frac{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 108821 by mathmax by abdo last updated on 19/Aug/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 174341 by behi834171 last updated on 31/Jul/22 $$\:\:\:\:\mathrm{1}.\underset{\:\:\:\:\mathrm{1}} {\overset{\:\:\:\:\:\:\:\:\:\:\mathrm{2}} {\int}}\:\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}−\mathrm{1}}\:}\:\boldsymbol{{dx}}=? \\ $$$$\:\:\:\:\:\mathrm{2}.\:\:\:\underset{\:\:\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\:\frac{\mathrm{2}\boldsymbol{{sinx}}+\mathrm{4}\boldsymbol{{cosx}}}{\boldsymbol{{sinx}}+\boldsymbol{{cosx}}}\:\:\boldsymbol{{dx}}=? \\ $$ Commented by mnjuly1970 last updated on 30/Jul/22…
Question Number 174336 by cortano1 last updated on 30/Jul/22 $$\:\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\:\frac{\mid{x}−\mathrm{2}\mid}{{x}^{\mathrm{2}} −\mathrm{4}{x}}\:{dx}\:=? \\ $$ Answered by Mathspace last updated on 30/Jul/22 $${I}=−\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}}…