Category: Integration

Question Number 87793 by M±th+et£s last updated on 06/Apr/20 $$showthat$$$$\int e^{sin\left(x\right)}dx=$$$$-\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}[cos\left(x\right)\ast {\left(sin\left(x\right)\right)}^{n+1}\ast {\left[{\left(sin\left(x\right)\right)}^2\right]}^{(\frac{-n}{2}-\frac{1}{2})}\ast 2F_1[\frac{1}{2},\frac{1-n}{2};\frac{3}{2};{\left(cos\left(x\right)\right)}^2]]+c$$$$ \…

Question Number 87769 by john santu last updated on 06/Apr/20 $$\int \frac{\ln ({\mathrm{e}}^{\mathrm{x}}+1)}{{\mathrm{e}}^{-\mathrm{x}}+1}\mathrm{dx}$$ Answered by TANMAY PANACEA. last updated on 06/Apr/20 $$\int\frac{{e}^{{x}} {ln}\left({e}^{{x}}…

Question Number 87757 by john santu last updated on 06/Apr/20 $${\int }_{\mathrm{a}}^{\mathrm{b}}\frac{\sqrt{\mathrm{x}-\mathrm{a}}}{\sqrt{\mathrm{b}-\mathrm{x}}}\mathrm{dx}=?$$ Commented by john santu last updated on 06/Apr/20 $$\left.\mathrm{let}\:\mathrm{x}\:=\:\mathrm{a}\:+\:\left(\mathrm{b}−\mathrm{a}\right)\:\mathrm{w}\:\right] \…

Question Number 87716 by Power last updated on 05/Apr/20 Commented by malwaan last updated on 05/Apr/20 $$putx=2siny\Rightarrow dx=2cosydy$$$$3x-x^3=2sin3y$$$$\therefore \int {}^3\sqrt{2sin3y}.2cosydy=??$$…

Question Number 87711 by M±th+et£s last updated on 05/Apr/20 $${\int }_0^{\mathrm{\infty }}\frac{1-{xe}^{-x}-e^{-x}}{x(e^x-e^{-x})}dx$$ Commented by mind is power last updated…