Category: Integration

Question Number 102690 by bramlex last updated on 10/Jul/20 $$\left(1\right)\int \frac{1}{\cos \sqrt{\mathrm{x}}}\mathrm{dx}$$$$\left(2\right)\int \frac{1}{2+\cot \mathrm{x}}\mathrm{dx}$$$$\left(3\right)\int \frac{1}{\ln \left(\cos \mathrm{x}\right)}\mathrm{dx}$$ Answered by Dwaipayan Shikari last updated on 10/Jul/20 $$\left.\mathrm{2}\right)\int\frac{{tanx}}{\mathrm{2}{tanx}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{tanx}+\mathrm{1}}{\mathrm{2}{tanx}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{1}}{\mathrm{2}{tanx}+\mathrm{1}}=\frac{{x}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}}{\left(\mathrm{2}{t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…

Question Number 168188 by cortano1 last updated on 05/Apr/22 $$\int \frac{1-\sin 2x}{{(1+\sin 2x)}^2}dx=?$$ Commented by Florian last updated on 09/Apr/22 $$?=\frac{1}{2\sqrt{2}}arctan\left(\sqrt{2}tan\left(2x\right)\right)+\frac{1}{4\sqrt{2}}(ln\mid \frac{1}{\sqrt{2}}cos\left(2x\right)+1\mid ln\mid \frac{1}{\sqrt{2}}cos\left(2x\right)-1\mid )+c,c\in R$$ Answered by…

Question Number 37079 by rahul 19 last updated on 08/Jun/18 Answered by ajfour last updated on 09/Jun/18 $$f{}^{″}\left(x\right)-3f{}^{\prime }\left(x\right)>3$$$$\Rightarrow f{}^{″}\left(0\right)>0$$$$forx>0f{}^{\prime }\left(x\right)>-1\dots .\left(i\right)$$$$\frac{{d}}{{dx}}\left[\:{f}\left({x}\right)+{x}\right]\:=\:{f}\:'\left({x}\right)+\mathrm{1}\: \…

Question Number 37071 by math khazana by abdo last updated on 08/Jun/18 $$findthevalueof{\int }_0^{\frac{\pi }{2}}\frac{xdx}{1+cosx}$$ Commented by math khazana by abdo last updated…

Question Number 37036 by ajfour last updated on 08/Jun/18 $${\int }_0^a(1-\frac{b-x}{\sqrt{{(b-x)}^2+cx}})dx=?$$ Commented by math khazana by abdo last updated on 09/Jun/18…