Category: Integration

Question Number 188982 by normans last updated on 10/Mar/23 Commented by normans last updated on 10/Mar/23 $$from\mathit{F}\mathit{B}difficultproblem$$ Commented by MJS_new last updated on…

Question Number 57899 by maxmathsup by imad last updated on 13/Apr/19 $$letf\left(x\right)={\int }_0^{+\mathrm{\infty }}\frac{dt}{{(t^2+x^2)}^3}withx>0$$$$1)findaexplicitformoff\left(x\right)$$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({t}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{3}} }\:\:{and}\:\int_{\mathrm{0}}…

Question Number 123387 by mnjuly1970 last updated on 25/Nov/20 $$\dots nicecalculus\dots$$$$provethat::$$$$\mathrm{\Omega }={\int }_0^1\frac{{\left(ln\left(x\right)\right)}^2{li}_3\left(x\right)}{1-x}dx$$$$\stackrel{???}{=}{\zeta }^2\left(3\right)-\zeta \left(6\right)✓$$ Commented…

Question Number 123361 by aristarque last updated on 25/Nov/20 $$pleasefindthe\int \frac{e^x}{x}dx$$ Commented by Dwaipayan Shikari last updated on 25/Nov/20 $$Ei\left(x\right)+C$$$${Or} \…

Question Number 188889 by mnjuly1970 last updated on 08/Mar/23 $$$$$$If,y=\frac{Arcsin\left(\sqrt{x}\right)}{\sqrt{x(1-x)}}\Rightarrow$$$$y^{\prime }.p\left(x\right)+y.q\left(x\right)=1$$$$$$$$find,{\int }_0^{1}p\left(x\right).q\left(x\right)dx=?$$$$p,qaretwopllynomils\dots$$$$ \…