Question Number 219449 by Lukos last updated on 25/Apr/25 $${L}\left\{{sinx}\right\}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} {sinx}\:{dx}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} \frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{i}}\left[\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}−{i}\right){x}} {dx}\:\:−\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}+{i}\right){x}}…
Question Number 219446 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\int{tan}\left(\frac{\frac{\mathrm{1}}{{n}}}{{sec}\left({n}\right)+\left(\frac{\mathrm{1}−{sec}\left({n}\right)}{{sec}\left({n}\right)}\right.}\right){dn} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219440 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\:\:{I}=\int\mathrm{tan}\left(\frac{\mathrm{cos}\left({n}\right)}{{n}\left(\mathrm{1}−\mathrm{cos}\left({n}\right)\:+\:\mathrm{cos}^{\mathrm{2}} \left({n}\right)\right)}\right)\:{dn} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219447 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Lim}_{{x}\rightarrow\infty} \underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\frac{−{x}}{{i}}\right)^{{i}} \\ $$$$ \\ $$ Answered by MrGaster last updated on…
Question Number 219434 by SdC355 last updated on 25/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219456 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \:\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +{x}_{\mathrm{4}}…
Question Number 219458 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \:{x}_{\mathrm{1}} ^{\:\mathrm{2}} {x}_{\mathrm{2}} ^{\:\mathrm{3}} {x}_{\mathrm{3}} ^{\:\mathrm{4}}…
Question Number 219428 by Nicholas666 last updated on 24/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\:,\:{b},\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\:−\infty} ^{\:\infty} \frac{\left({e}^{{iax}} −\mathrm{1}\right)\left({e}^{{ibx}} −\mathrm{1}\right)}{{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$ Commented by…
Question Number 219384 by mnjuly1970 last updated on 23/Apr/25 Answered by SdC355 last updated on 24/Apr/25 $$\int\:\:\:\frac{\mathrm{d}{x}}{\:\sqrt{{x}}}\:\mathrm{cos}^{\mathrm{3}} \left({x}\right)\mathrm{sin}\left({x}\right)={I} \\ $$$$\int\:\:\:\frac{\mathrm{d}{x}}{\:{x}}\:\sqrt{{x}}\mathrm{cos}^{\mathrm{3}} \left({x}\right)\mathrm{sin}\left({x}\right)=\int\:\:\:\frac{\mathrm{d}{x}}{{x}}\:\sqrt{{x}}\mathrm{cos}^{\mathrm{2}} \left({x}\right)\mathrm{cos}\left({x}\right)\mathrm{sin}\left({x}\right) \\ $$$$\int\:\:\frac{\mathrm{d}{x}}{\:\mathrm{2}{x}}\:\sqrt{{x}}\mathrm{cos}^{\mathrm{2}} \left({x}\right)\mathrm{sin}\left(\mathrm{2}{x}\right)=\int\:\:\mathrm{d}{x}\:\frac{{e}^{−{xt}}…
Question Number 219316 by Nicholas666 last updated on 23/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Prove}; \\ $$$$\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\infty} \frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}^{\lfloor\boldsymbol{{x}}\rfloor} } \:+\:\left\{{x}\right\}}\:{dx}\:=\:{ln}\mathrm{2}\:\:\: \\ $$ Answered by vnm last updated…