Category: Integration

Question Number 122927 by bemath last updated on 21/Nov/20 Commented by liberty last updated on 21/Nov/20 $$\mu \left(x\right)=\int \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}dx$$$$[let\sqrt{x}=\sin z\Rightarrow dx=\sin 2zdz]$$$$\mu \left(x\right)=\int \sqrt{\frac{1-\sin z}{1+\sin z}}\left(\sin 2zdz\right)$$$$\mu\left({x}\right)=\int\:\frac{\sqrt{\left(\mathrm{1}−\mathrm{sin}\:{z}\right)^{\mathrm{2}} }}{\mathrm{cos}\:{z}}\:\left(\mathrm{2sin}\:{z}\:\mathrm{cos}\:{z}\:\right)\:{dz} \…

Question Number 122922 by bemath last updated on 21/Nov/20 $$\underset{0}{\stackrel{\pi /4}{\int }}\frac{\cos x+\sin x}{16\sin 2x+9}dx$$ Answered by liberty last updated on 21/Nov/20 $$\varsigma\:=\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{16sin}\:\mathrm{2}{x}+\mathrm{9}}\:{dx}\: \…

Question Number 122919 by bemath last updated on 20/Nov/20 Answered by Dwaipayan Shikari last updated on 20/Nov/20 $${\int }_0^{\frac{1}{2}}\frac{{xe}^{2x}}{{(1+2x)}^2}dx$$$$=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 122884 by CanovasCamiseros last updated on 20/Nov/20 Commented by CanovasCamiseros last updated on 20/Nov/20 $$\mathit{N}\mathit{e}\mathit{e}\mathit{d}\mathit{h}\mathit{e}\mathit{l}\mathit{p}\mathit{f}\mathit{o}\mathit{r}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}$$ Answered by MJS_new last updated on…

Question Number 122875 by pipin last updated on 20/Nov/20 $$\int \frac{({\mathbf{x}}^2+1)\mathbf{dx}}{{\mathbf{x}}^4+{\mathbf{x}}^2+1}=\dots$$$$$$ Answered by som(math1967) last updated on 20/Nov/20 $$\int\frac{\frac{\mathrm{x}^{\mathrm{2}}…