Category: Integration

Question Number 42605 by maxmathsup by imad last updated on 28/Aug/18 $$letf\left(x\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{arctan\left({xt}^2\right)}{1+2t^2}dt$$$$1)findaexpliciteformoff\left(x\right)$$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left({t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\infty}…

Question Number 42593 by aseerimad last updated on 28/Aug/18 Commented by maxmathsup by imad last updated on 28/Aug/18 $${we}\:{have}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cos}^{\mathrm{4}} {x}\:+{sin}^{\mathrm{4}} \:{x}−{sin}^{\mathrm{4}} {x}}{{sin}^{\mathrm{4}} {x}\:+{cos}^{\mathrm{4}}…

Question Number 42579 by Raj Singh last updated on 28/Aug/18 $$\int sinx/\sqrt{1+sinx}$$ Commented by maxmathsup by imad last updated on 28/Aug/18 $$letA=\int \frac{sinx}{\sqrt{1+sinx}}dxwehave1+sinx=1+2sin\left(\frac{x}{2}\right)cos\left(\frac{x}{2}\right)$$$$=\left({sin}\left(\frac{{x}}{\mathrm{2}}\right)\:+{cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}}…

Question Number 108095 by bemath last updated on 14/Aug/20 $$\frac{\mathrm{\infty }\mathcal{B}e\mathcal{M}ath\mathrm{\infty }}{\mathrm{♠}}$$$$\int 2x{\cos }^{-1}\left(x\right)dx$$ Answered by bemath last updated on 14/Aug/20 Answered by Dwaipayan…

Question Number 108073 by bemath last updated on 14/Aug/20 $$\frac{\triangleq \mathcal{B}e\mathcal{M}ath\triangleq }{\prec }$$$$\int \frac{xdx}{x^8-1}?$$ Answered by john santu last updated on 14/Aug/20 $$\:\:\:\:\frac{\Box\mathcal{JS}\boxdot}{≢} \…