Category: Integration

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}…

Question Number 164682 by Zaynal last updated on 20/Jan/22 $$\int 27{\mathit{x}}^2\sqrt{3\mathit{x}-2}\mathit{d}\mathit{x}$$ Answered by Ar Brandon last updated on 20/Jan/22 $$=3\int {(3x-2+2)}^2\sqrt{3x-2}dx$$$$=\mathrm{3}\int\left(\left(\mathrm{3}{x}−\mathrm{2}\right)^{\frac{\mathrm{5}}{\mathrm{2}}}…

Question Number 33599 by abdo imad last updated on 19/Apr/18 $$calculatef\left(a\right)={\int }_{-a}^a\frac{dx}{{(t^2+x^2)}^{\frac{3}{2}}}witha>0.$$ Commented by abdo imad last updated on…

Question Number 33589 by abdo imad last updated on 19/Apr/18 $$1)decomposeF\left(x\right)=\frac{1}{(x^2+4){(x-3)}^2}$$$$2)calculate{\int }_4^{+\mathrm{\infty }}\frac{dx}{(x^2+4){(x-3)}^2}.$$ Commented by math khazana…