Category: Integration

Question Number 92407 by mathmax by abdo last updated on 06/May/20 $$letf\left(a\right)={\int }_0^{1}ln(\sqrt{1+x}+a\sqrt{1-x})dxwitha>0$$$$1)explicitef\left(a\right)$$$$2)findg\left(a\right)={\int }_0^1\frac{\sqrt{1-x}}{\sqrt{1+x}+a\sqrt{1-x}}dx$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\mathrm{2}\sqrt{\mathrm{1}−{x}}\right){dx} \…

Question Number 157929 by akolade last updated on 30/Oct/21 $$\int \frac{\mathrm{dx}}{\sin \mathrm{x}+\sec \mathrm{x}}$$$$\mathrm{using}\mathrm{wiestress}\mathrm{substitution}$$ Commented by cortano last updated on 30/Oct/21 $$C=\int \frac{1}{\sin x+\sec x}dx$$$$\:\left[\:\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:=\:{u}\:\rightarrow\begin{cases}{\mathrm{sin}\:{x}\:=\frac{\mathrm{2}{u}}{\mathrm{1}+{u}^{\mathrm{2}} }}\{\mathrm{cos}\:{x}=\frac{\mathrm{1}−{u}^{\mathrm{2}}…

Question Number 92394 by john santu last updated on 06/May/20 $$\int \ln (\sqrt{1-x}+\sqrt{1+x})dx$$ Commented by mathmax by abdo last updated on 06/May/20 $$I=\int ln(\sqrt{1-x}+\sqrt{1+x})dxbyparts$$$${I}\:={x}\left(\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\right)−\int\:{x}\frac{\left(\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\right)^{'}…

Question Number 92334 by Power last updated on 06/May/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 92323 by Power last updated on 06/May/20 Commented by Prithwish Sen 1 last updated on 06/May/20 $$\mathrm{split}\mathbf{x}+3\mathbf{into}\frac{1}{8}(8\mathbf{x}+4)+\frac{5}{2}$$ Commented by Power last…