Category: Integration

Question Number 99173 by bemath last updated on 19/Jun/20 Answered by MJS last updated on 19/Jun/20 $$\mathrm{this}\mathrm{is}\mathrm{very}\mathrm{complicated}$$$$\int \sqrt{\frac{1+\cot x}{\csc x+\cot x}}dx=\int \sqrt{\frac{\sin x+\cos x}{1+\cos x}}dx=$$$$[t=\tan \frac{x}{2}\to dx={2\cos }^2\frac{x}{2}dt]$$$$=\sqrt{\mathrm{2}}\int\frac{\sqrt{−{t}^{\mathrm{2}} +\mathrm{2}{t}+\mathrm{1}}}{{t}^{\mathrm{2}}…

Question Number 33619 by NECx last updated on 20/Apr/18 $$\int x^{5/2}{(1-x)}^{3/2}dx$$ Commented by abdo imad last updated on 20/Apr/18 $${let}\:{put}\:{I}\:=\:\int\:\:{x}^{\frac{\mathrm{5}}{\mathrm{2}}} \:\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \:{dx}\:\:.{ch}.{x}={sin}^{\mathrm{2}}…

Question Number 164685 by Zaynal last updated on 20/Jan/22 $$\int 4{\mathit{x}}^2{(1-\mathit{x})}^3\mathit{d}\mathit{x}$$ Answered by Ar Brandon last updated on 20/Jan/22 $$=\mathrm{4}\int\left(\mathrm{1}−{x}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{3}} {dx}…

Question Number 164684 by Zaynal last updated on 20/Jan/22 $$\int 24{(2\mathit{x}-1)}^{-3}\mathit{d}\mathit{x}$$ Answered by Ar Brandon last updated on 20/Jan/22 $$=\int\frac{\mathrm{24}}{\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{3}} }{dx}=−\frac{\mathrm{6}}{\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} }+{C} \…

Question Number 164681 by Zaynal last updated on 20/Jan/22 $$\int (-8\mathit{x}\sqrt{3-2\mathit{x}})\mathit{d}\mathit{x}$$ Answered by Ar Brandon last updated on 20/Jan/22 $$=4\int (3-2x-3)\sqrt{3-2x}dx$$$$=\mathrm{4}\int\left(\left(\mathrm{3}−\mathrm{2}{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{3}\left(\mathrm{3}−\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right){dx}…