Question Number 144220 by Mathspace last updated on 23/Jun/21 $${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{{n}} \right){dx} \\ $$$${n}\:\in{N} \\ $$ Answered by mathmax by abdo last updated…
Question Number 144217 by Mathspace last updated on 23/Jun/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{\mathrm{2}} }{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left(\mathrm{3}{x}+\mathrm{1}\right)^{\mathrm{4}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78685 by berket last updated on 19/Jan/20 $${is}\:{g}\:=\left\{\left(\mathrm{1}.\:\mathrm{1}\right).\left(\mathrm{2}.\mathrm{3}\right).\left(\mathrm{3}\:.\mathrm{5}\right).\left(\mathrm{4}.\mathrm{7}\right)\right\}\:{a}\:{function}?\:{justify}\:{if}\:{this}\:{is}\:{described}\:{by}\:{the}\:{relation}\:{g}\left({x}\right)={ax}+{b}\:{then}\:{what}\:{values}\:{should}\:{be}\:{assigned}\:{to}\:{a}\:{and}\:{b}\:? \\ $$ Commented by mr W last updated on 19/Jan/20 $${sir}:\:{please}\:{don}'{t}\:{type}\:{the}\:{whole}\:{post}\:{in} \\ $$$${one}\:{single}\:{line}!\:{it}'{s}\:{terrible}\:{to}\:{read}! \\ $$…
Question Number 144222 by Mathspace last updated on 23/Jun/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{2}} {x}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144216 by Mathspace last updated on 23/Jun/21 $${find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{2}}} \\ $$ Answered by bemath last updated on 23/Jun/21 $$\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{2}}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{2}}}\:=\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{2}}−\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 144219 by Mathspace last updated on 23/Jun/21 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\left(\mathrm{2}+{cosx}\right)^{\mathrm{2}} } \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21 $$\mathrm{let}\:\varphi\left(\mathrm{a}\right)=\frac{\mathrm{1}}{\mathrm{a}+\mathrm{cosx}}\:\:\mathrm{with}\:\mathrm{a}>\mathrm{1}\:\Rightarrow\varphi^{'}…
Question Number 144213 by Mathspace last updated on 23/Jun/21 $${find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{cosx}+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Answered by bemath last updated on 23/Jun/21 $$\int\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}+\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}} \\ $$$$=\:\int\:\frac{\mathrm{dx}}{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{x}} \\…
Question Number 144218 by Mathspace last updated on 23/Jun/21 $${U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{k}+\mathrm{1}}} \\ $$$${find}\:{a}\:{eqivalent}\:{of}\:{U}_{{n}} \left({n}\rightarrow\infty\right) \\ $$ Answered by ArielVyny last updated on 24/Jun/21…
Question Number 144212 by Mathspace last updated on 23/Jun/21 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} +\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144215 by Mathspace last updated on 23/Jun/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}} \sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com