Question Number 124920 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{n}} } \mathrm{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 124921 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\mathrm{z}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}\:\:\mathrm{with}\:\mathrm{z}\:\mathrm{complex} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124919 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{n}} \mathrm{arctan}\left(\mathrm{x}\right)\mathrm{dx}\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{nstural} \\ $$ Commented by mindispower last updated on 07/Dec/20…
Question Number 59381 by Karan last updated on 09/May/19 $$\:\:\int\frac{{xdx}}{\mathrm{sin}\:{x}}\:=\:? \\ $$ Commented by Mr X pcx last updated on 11/May/19 $${let}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\frac{{t}}{{sint}}{dt}\:{we}\:{have}\: \\…
Question Number 124906 by Mammadli last updated on 06/Dec/20 $$\int\boldsymbol{{sinx}}^{\mathrm{3}} \boldsymbol{{dx}}=? \\ $$ Commented by Dwaipayan Shikari last updated on 06/Dec/20 $$\int{sinx}^{\mathrm{3}} {dx}\:\:\:\:\:\:\:\:\:\: \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{i}}\int{e}^{{ix}^{\mathrm{3}}…
Question Number 124903 by Algoritm last updated on 06/Dec/20 Answered by MJS_new last updated on 06/Dec/20 $$\mathrm{just}\:\mathrm{decompose}\:\mathrm{and}\:\mathrm{solve},\:\mathrm{no}\:\mathrm{special} \\ $$$$\mathrm{knowledge}\:\mathrm{necessary}.\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}: \\ $$$$\frac{{x}−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid{x}+\mathrm{1}\mid\:+{C} \\ $$$$\mathrm{now}\:\mathrm{try}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself}…
Question Number 124888 by mnjuly1970 last updated on 06/Dec/20 $$:::::\:\:{prove}\:{that}\: \\ $$$$\:\:::::\:\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\infty} \frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\:\sqrt{\mathrm{2}}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$ Answered by mnjuly1970…
Question Number 124887 by mnjuly1970 last updated on 06/Dec/20 $$\:\:\:\:\:…{nice}\:\:{calculus}.. \\ $$$$\:\:\:{evaluate}\:: \\ $$$$\:\:\mathrm{2}\int_{\mathrm{1}} ^{\:\infty} \left(\frac{\left\{{x}\right\}−\frac{\mathrm{1}}{\mathrm{2}}}{{x}}\right){dx}−\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){dx}=??? \\ $$$$\left\{{x}\right\}:\:{fractional}\:{part}… \\ $$ Answered by Dwaipayan…
Question Number 190419 by horsebrand11 last updated on 02/Apr/23 $$\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\underset{−\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} {\overset{\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} {\int}}\:\mathrm{ln}\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}\right){dx}\:{dy}\:=? \\ $$ Answered by witcher3 last updated…
Question Number 59344 by rahul 19 last updated on 08/May/19 $$\int\:{e}^{{x}} \left(\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\right){dx}\:=\:? \\ $$ Answered by MJS last updated on 08/May/19 $$\mathrm{the}\:\mathrm{trick}\:\mathrm{is}\:\mathrm{this}: \\ $$$$\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:{x}}−\frac{\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{2sin}^{\mathrm{2}} \:\frac{{x}}{\mathrm{2}}}−\frac{\mathrm{1}}{\mathrm{tan}\:\frac{{x}}{\mathrm{2}}}=…