Category: Integration

Question Number 155217 by talminator2856791 last updated on 27/Sep/21 $$$$$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{\ln \left(\sqrt{x^4+1}\right)}{\sqrt{x^4+1}}dx$$$$$$ Terms of Service Privacy Policy…

Question Number 89636 by jagoll last updated on 18/Apr/20 $$\int \frac{\cos \mathrm{x}+\sin \mathrm{x}}{\sin 2\mathrm{x}}\mathrm{dx}$$ Commented by M±th+et£s last updated on 18/Apr/20 $$A=\int \frac{1}{cos\left(x\right)}+tan\left(x\right)-tan\left(x\right)dx$$$$\int \frac{1+sin\left(x\right)}{cos\left(x\right)}dx-\int \frac{sin\left(x\right)}{cos\left(x\right)}dx$$$$\int\frac{{cos}\left({x}\right)}{\mathrm{1}−{sin}\left({x}\right)}{dx}−\int\frac{{sin}\left({x}\right)}{{cos}\left({x}\right)}{dx} \…

Question Number 155146 by amin96 last updated on 26/Sep/21 $$\mathcal{L}={\int }_0^1{\int }_0^1{\int }_0^1{\left(\left\{\frac{x}{y}\right\}\left\{\frac{y}{z}\right\}\left\{\frac{z}{x}\right\}\right)}^{n}dxdydz=?$$ Answered by yeti123 last updated on…

Question Number 89596 by A8;15: last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\sqrt{\frac{x}{1-x}}=t\Rightarrow x=\frac{t^2}{t^2+1}$$$$\left.{dx}\:=\:\frac{\mathrm{2}{t}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt}\:\right]\: \…

Question Number 89593 by M±th+et£s last updated on 19/Apr/20 $$showthat$$$${\int }_0^{\frac{\pi }{2}}ln\left(sec\left(x\right)\right)ln\left(csc\left(x\right)\right)dx=\frac{{\pi }^2{ln}^2\left(2\right)}{2}-\frac{{\pi }^4}{48}$$ Commented by maths mind last updated…