Question Number 31967 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctanx}}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}{dx}\:. \\ $$ Commented by abdo imad last updated on 19/Mar/18 $${let}\:{put}\:{I}\:=\int_{\mathrm{0}}…
Question Number 31951 by NECx last updated on 17/Mar/18 $${Evaluate}\:\int\mathrm{sin}\:\sqrt{{x}}{dx} \\ $$ Answered by mrW2 last updated on 17/Mar/18 $${u}=\sqrt{{x}} \\ $$$${du}=\frac{{dx}}{\mathrm{2}\sqrt{{x}}}=\frac{{dx}}{\mathrm{2}{u}} \\ $$$${dx}=\mathrm{2}{udu} \\…
Question Number 163008 by tounghoungko last updated on 03/Jan/22 $$\:{Calculate}\: \\ $$$$\:\:\:\int\:\frac{\left(\mathrm{2}−\mathrm{4sin}\:{x}\:\mathrm{cos}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \mathrm{2}{x}+\mathrm{64}\:\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}}\:{dx}\: \\ $$$$ \\ $$ Answered by som(math1967) last updated on 03/Jan/22…
Question Number 97439 by bemath last updated on 08/Jun/20 $$\underset{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{6x}}\right)\sqrt{\mathrm{1}+\left(\frac{\mathrm{3x}^{\mathrm{2}} }{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{6x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$ Commented by john santu last updated on…
Question Number 97417 by MJS last updated on 08/Jun/20 $$\int\frac{{x}}{{a}+\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=? \\ $$ Answered by MJS last updated on 08/Jun/20 $$\mathrm{just}\:\mathrm{found}\:\mathrm{a}\:\mathrm{path}: \\ $$$$\mathrm{sin}\:{x}\:=\frac{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{e}^{−\mathrm{i}{x}} }{\mathrm{2i}}…
Question Number 97400 by student work last updated on 07/Jun/20 $$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$$$\:\:\mathrm{help}\:\mathrm{me} \\ $$ Commented by Tony Lin last updated on 08/Jun/20 $${sinx}=\frac{{e}^{{ix}}…
Question Number 31858 by NECx last updated on 16/Mar/18 $$\int\frac{{sinx}}{{x}}{dx} \\ $$ Commented by abdo imad last updated on 18/Mar/18 $${we}\:{have}\:{sinx}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} \:}{\left(\mathrm{2}{n}+\mathrm{1}\right)!}\:{x}^{\mathrm{2}{n}+\mathrm{1}} \:\:{with}\:{radius}\:{R}=\infty…
Question Number 31839 by Joel578 last updated on 15/Mar/18 $${I}\:=\:\int\:\sqrt{{x}\:+\:\sqrt{{x}^{\mathrm{2}} \:−\:\mathrm{1}}}\:{dx} \\ $$ Commented by Joel578 last updated on 15/Mar/18 $$\:\:\:=\:\int\:\sqrt{{x}\:+\:\sqrt{\mathrm{4}\:.\:\frac{{x}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{4}}}}\:{dx} \\ $$$$\:\:\:=\:\int\:\sqrt{\frac{{x}\:+\:\mathrm{1}}{\mathrm{2}}\:+\:\frac{{x}\:−\:\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}\sqrt{\frac{\left({x}\:+\mathrm{1}\right)\left({x}\:−\:\mathrm{1}\right)}{\mathrm{2}\:.\:\mathrm{2}}}}\:{dx} \\…
Question Number 31838 by Joel578 last updated on 15/Mar/18 $$\mathrm{Given} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{16}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}\right){x}^{\mathrm{2}} \:−\:\frac{\mathrm{9}}{\mathrm{10}}\left(\int_{\mathrm{0}} ^{\mathrm{2}} \:{f}\left({x}\right){dx}\right){x}\:+\:\mathrm{2}\left(\int_{\mathrm{0}} ^{\mathrm{3}} \:{f}\left({x}\right){dx}\right)\:+\:\mathrm{4} \\ $$$$\mathrm{Solve} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{t}\:+\:\left(\int_{{f}\left(\mathrm{2}\right)\:+\:\mathrm{2}} ^{{f}^{−\mathrm{1}}…
Question Number 97361 by student work last updated on 07/Jun/20 $$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$ Commented by student work last updated on 07/Jun/20 $$\mathrm{who}\:\mathrm{is}\:\mathrm{intellagent}? \\ $$…