Category: Integration

Question Number 63508 by mathmax by abdo last updated on 05/Jul/19 $$letf\left(x\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dt}{(t^2+ixt-1)}with\mid x\mid >2(i^2=-1)$$$$1)extractRe\left(f\left(x\right)\right)andIm\left(f\left(x\right)\right)$$$$2)calculatef\left(x\right)$$$$\left.\mathrm{3}\right)\:\:{find}\:{olso}\:{g}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{t}}{\left({t}^{\mathrm{2}} \:+{ixt}\:−\mathrm{1}\right)^{\mathrm{2}}…

Question Number 129038 by bramlexs22 last updated on 12/Jan/21 $$\int \frac{{5\mathrm{e}}^{4\mathrm{t}}+{10\mathrm{e}}^{2\mathrm{t}}+2}{{\mathrm{e}}^{2\mathrm{t}}+2}\mathrm{dt}$$ Answered by liberty last updated on 12/Jan/21 $$\:\int\:\frac{\left(\mathrm{5e}^{\mathrm{2t}} +\mathrm{1}\right)\left(\mathrm{e}^{\mathrm{2t}} +\mathrm{2}\right)−\mathrm{e}^{\mathrm{2t}}…

Question Number 129033 by oustmuchiya@gmail.com last updated on 12/Jan/21 $$proveusingthefirstprinciplethat$$$$thederivativeof\mathit{s}\mathit{i}\mathit{n}\mathit{x}is\mathit{c}\mathit{o}\mathit{x}\mathit{x}and$$$$thatthederivativeof\mathit{c}\mathit{o}\mathit{s}\mathit{x}is$$$$-\mathit{s}\mathit{i}\mathit{n}\mathit{x}$$ Commented by bramlexs22 last updated on 12/Jan/21…

Question Number 129009 by bramlexs22 last updated on 12/Jan/21 $$\mathrm{Given}\mathrm{f}(\mathrm{x}+1)=\frac{1+\mathrm{f}\left(\mathrm{x}\right)}{1-\mathrm{f}\left(\mathrm{x}\right)};\mathrm{f}\left(2\right)=2$$$$\mathrm{and}{\int }_2^{2018}\mathrm{x}.\mathrm{f}\left(2018\right)\mathrm{dx}=2^{\mathrm{a}}.3^{\mathrm{b}}.5^{\mathrm{c}}.7^{\mathrm{d}}.{11}^{\mathrm{e}}.{101}^{\mathrm{f}}$$$$\mathrm{then}\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}=\mathrm{\_}\mathrm{\_}$$ Answered by…

Question Number 128985 by bramlexs22 last updated on 11/Jan/21 $$\int \ln \left(\tan \mathrm{x}\right)\ln \left(\sin \mathrm{x}\right)\mathrm{dx}?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com