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Question Number 193377 by Humble last updated on 12/Jun/23 $${Evaluate} \\ $$$${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by Frix last updated…
Question Number 193278 by Nimnim111118 last updated on 09/Jun/23 $${Please}\:{Help}…!! \\ $$$$\:\:\:\:\underset{\:\:\:\:\mathrm{0}} {\int}^{\:\:\infty} {x}.{e}^{−{x}} .{sinx}.{dx}\: \\ $$$$ \\ $$ Answered by qaz last updated on…
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Question Number 193214 by Humble last updated on 07/Jun/23 $${Evaluate} \\ $$$$\Omega=\int_{−\infty} ^{\:\infty} \frac{{e}^{\frac{{x}}{\mathrm{2}}} {ln}\left(\sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\right)}{{tanh}^{−\mathrm{1}} \left(\frac{{x}}{\mathrm{3}}\right)\left(\mathrm{1}+{e}^{{x}} \right)}{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 193231 by C2coder last updated on 07/Jun/23 Answered by leodera last updated on 08/Jun/23 $${F}\left({a}\right)\:=\:\int_{−\infty} ^{\infty} \frac{{e}^{−{x}^{\mathrm{2}} } \mathrm{sin}\:^{\mathrm{2}} \left({ax}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\…
Question Number 131068 by EDWIN88 last updated on 01/Feb/21 $$\:\int\:\mathrm{sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:\mathrm{4}{x}\:{dx}\:=?\: \\ $$ Answered by Ar Brandon last updated on 01/Feb/21 $$\mathcal{I}=\int\mathrm{sin}^{\mathrm{2}} \mathrm{xcos4xdx}=\frac{\mathrm{1}}{\mathrm{2}}\int\left(\mathrm{1}+\mathrm{cos2x}\right)\mathrm{cos4xdx} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int\left[\mathrm{cos4x}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos6x}+\mathrm{cos2x}\right)\right]\mathrm{dx}…
Question Number 131058 by pipin last updated on 01/Feb/21 $$\int\frac{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{5}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{6}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{7}\right)}\:\mathrm{dx}\: \\ $$ Answered by MJS_new last updated on 01/Feb/21…
Question Number 131053 by pipin last updated on 01/Feb/21 $$\int\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 01/Feb/21 $$\mathcal{I}=\int\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\mathrm{dx}=\int\frac{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}}…
Question Number 131050 by mathmax by abdo last updated on 31/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{tsin}\left(\mathrm{xt}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dt}\:\:\:\left(\mathrm{x}>\mathrm{0}\right) \\ $$$$\mathrm{calculate}\:\mathrm{f}^{'} \left(\mathrm{x}\right) \\ $$ Answered by mathmax…